Блог Анкара

In This Chapter

^ Figuring the distance traveled as the sum of two different distances ^ Equating two distances that have different rates of speed ^ Emptying or filling a tank with open intake and outflow valves ^ Divvying up the work with work problems

His chapter deals with a lot of moving around. People and cars and trains

Are moving around all the time. Liquids in containers are moving from one place to another. The first problems involve moving around and the distance traveled. The typical distance problems use the relationship that distance is equal to rate times time, D = Rt. By using this equation, you deal with trains meeting somewhere in the middle of nowhere and wives catching up to forgetful husbands.

Another type of moving around occurs with the classic work problems — how many hands it takes for a lighter workload — and how long it takes when everyone works together.

And, lastly, you’ll find a lot of moving around when fluids move from one container to an other. If you’re trying to fill a tub while the tub is leaking, you have to work quickly to find out how long it takes to actually make the tub overflow.

Summing Up the Distances

These first distance problems have a common theme: that the sum of the distances that two people travel, along the same straight line, equals the total distance. Sometimes, people are traveling toward one another, and the sum

Of the distances is how far each has traveled until they meet. Other times, people are traveling in opposite directions, and you sum up the distances traveled to compute how far apart they are.

Meeting somewhere in the middle

Two lovers spy each other on opposite sides of the room and run toward one another. They meet somewhere between where they started running — and where they meet depends on how fast each can run. You can assume that there are no chairs to dodge in their mad dashes. The setup used to solve this problem is pretty much the same as a problem involving two bulls rushing at one another from either side of the arena or two trains approaching one another from opposite directions along the same track.

Keep in mind the formula D = Rt Or Distance = Rate X Time. When two different distances are added together to equal a total distance, the individual rates and times are multiplied together first and then the products are added together:

D = d, + d2

Making good time

With distance problems, you can solve for the distance traveled or the speed at which objects are traveling or the amount of time spent. The two problems in this section involve solving for how much time it takes to reach a goal.

The Problem: Betsy and Bart see each other from opposite sides of a gymnasium that measures 440 feet across. They both start running toward one another at the same time. If Betsy can run at the rate of 4 feet per second and Bart runs at 7 feet per second, then how long does it take for them to meet?

The total distance to be covered is 440 feet. Set that amount equal to the sum of the distances that each runner covers. Betsy can run at the rate of 4 feet per second, and she runs for T Seconds. Bart can run at 7 feet per second and also runs for T Seconds. So your equation is 440 = 4t + 7t. Simplify on the right to get 440 = ,,t. Divide each side of the equation by,,, and you get that T = 40 seconds. It’ll take less than a minute for the two to reach one another, with Betsy running 4(40) = 160 feet and Bart running 7(40) = 280 feet.

In the preceding problem, the two people see each other and start running at the same time. What if one starts before the other, and they run for different amounts of time?

The Problem: Jon leaves Chicago at noon and heads south toward Bloomington traveling at 45 mph. Jane leaves Bloomington heading north for Chicago at 1 p. m., traveling at 55 mph. If Chicago and Bloomington are,45 miles apart, then what time will they meet?

^VLA* The total distance to be traveled is 145 miles. If Jon drives for T Hours, then Jane, who left an hour later, will drive for T - 1 hours. Take each rate in terms of miles per hour and multiply it by the respective amount of time traveled. Jon will drive for 45T Miles and Jane will travel for 55(t - 1) miles. Add the two distances together and set the sum equal to 145. Solve the equation for T.

45t + 55 (T – 1) = 145 45t + 55t – 55 = 145 100T -55 =145 100T = 200 T= 2

Because T Is the number of hours that Jon drives, he drives for two hours and Jane drives for one hour less or one hour. In any case, they meet up at 2 p. m.

Speeding things up

Distance is equal to rate times time. Participants in these distance problems may travel for the same amount of time or different amounts of time. They can travel at the same speed or different speeds. The next two problems let you determine how fast things are moving.

The Problem: Two trains leave the same station traveling in opposite directions. The first train leaves at 2 p. m. The second train leaves a half-hour later and travels at a speed averaging 15 miles per hour faster than the first train. By 8 o’clock that evening, they’re 600 miles apart. How fast are the two trains traveling?

Vjj. VLA/V Use the same D = Rt Format, setting the sum of the distances traveled equal to 600. The first train travels for 6 hours at rate r, and the second train, leaving a half-hour later, only travels for 5.5 hours but at a greater speed, R + 15. The equation and solution:

6r + 5.5 (R + 15) = 600 6r + 5.5r + 82.5 = 600 11.5r + 82.5 = 600

11.5r = 517.5 517.5 11.5

The first train is traveling at 45 mph. The faster, or 60 mph.

Second train is traveling 15 mph

Taxi driver

Imagine that you’re a taxi driver in Chicago and 30 mph, and the tank is half full of fuel. One mile

That you’re driving a 1994 yellow cab. Your pas- into the trip, the tank is down to two-fifths full of

Sengers are college students, and they want to fuel, and the trip is over 15 minutes later. What is

Travel 4 miles from home to school. You’re driving the name and age of the cab driver?

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The Problem: Alberto can bicycle 2 miles per hour less than twice as fast as Ollie, so Alberto didn’t leave for the rally until two hours after Ollie left. If the total distance they traveled was 504 miles and if Ollie traveled for 10 hours, then how fast can Alberto bicycle?

Let the rate at which Ollie can bicycle be r. Then Alberto’s rate is 2r – 2. If Ollie traveled for 10 hours, then Alberto traveled for 8 hours. The total distance is equal to the sum of the distances the two traveled. Ollie traveled 10R Miles, and Alberto traveled 8(2R - 2) miles.

10r + 8 (2r – 2) = 504 10r + 16r – 16 = 504 26R -16 =504 26R = 520

R 520

26

Ollie bicycles at 20 mph, so Alberto bicycles at 2(20) – 2 = 40 – 2 = 38 mph.

Making a beeline

You can solve for the time it takes to travel, and you can solve for how fast cars or trains travel. Determining the total distance that someone or something travels can also be very interesting. Consider the story of Super Bee Who flies at the speed of 90 mph. He leaves the engine of a westbound train that’s traveling at 60 mph and flies until he reaches an eastbound train that’s traveling at 75 mph along the same track. After barely touching the east-bound train, he flies back to the westbound train, touches it, and flies back

And forth and back and forth between the trains until the trains finally meet. Figure 16-1 shows you the two trains and Super Bee, Flying between them.

Figure 16-1:

Super Bee flies back and forth between the speeding trains

The Problem: How far does a bee travel if it flies back and forth between trains that are approaching each other on the same track — one train traveling at 60 mph and the other traveling 75 mph — if the bee flies at 90 mph and, when it started this journey, the trains were 648 miles apart?

You could determine how far the bee had to fly until it flew from the first train to the second train — while the trains are getting closer to one another — and then how far it had to fly back to the first train, and so on, until the trains meet. Or, a much simpler way to do this is to figure out how long it will take the trains to meet if they start 648 miles apart and are approaching each other at the rate of 135 mph (the sum of 60 mph and 75 mph). When you’ve determined how much time it takes, then you know how long the bee has been flying and can multiply the time and the rate of 90 mph to get the distance. Because D = Rt, In this case 648 = 135t. Dividing each side of the equation by 135, you get that T = 4.8 hours — the time it takes the trains to meet. Multiplying 90 x 4.8, you get a distance of 432 miles. That’s one tired bee.

Equating the Distances Traveled

Many distance problems have the scenario that one person catches up with another or one train or plane leaves later and finally passes the first one. The common thread or theme for these problems is that the distance traveled by the two participants is the same. You equate the distances. Some problems have you solve for time — how long it took to catch up. Or you may solve for how fast one or the other is traveling. And the question may even be about the distance — how far they traveled before arriving at the same place. In each case, though, the equation setup is the same.

7

The formula is D = Rt Or Distance = Rate X Time. And when two distances are equated, the individual rates and times are multiplied together first and then set equal to one another:

Making it a matter of time

When two people leave the same place at different times, one has to travel more quickly than the other to catch up — assuming that they’re both using the same route.

The Problem: Henry left for work at 7 a. m. and drove at an average speed of 45 mph. Unfortunately, he forgot to put some important papers in his briefcase. At 7:30, Betty found the papers, jumped in her car, and chased after Henry. She averaged 55 mph. How long did it take for Betty to catch up to Henry?

^VLA/V The distance that Henry drives and the distance that Betty drives is the

Same — at the moment Betty catches up to Henry. So multiply the rate that Henry drives times how long he drives and equate that to the rate that Betty drives times her amount of time. Let the amount of time that Henry drives be represented by T Hours. Then Betty drives for T - 0.5 hours. Multiplying rate times time, the equation and solution are:

45T=55(t-0.5) 45T=55T-27.5

27.5 = 10T

T=Nrr = 2.75

Henry drove for 2.75 hours, or 2 hours and 45 minutes. If Betty drove for half an hour less than that, she drove for 2 hours and 15 minutes.

You can solve directly for the amount of time that Betty traveled by letting Betty’s time be T And Henry’s time be T + 0.5. The equation is just a bit different, but the answer will still come out that Betty drove for 2.25 or 2 hours and 15 minutes.

In the classic story of the tortoise and the hare, the tortoise is slow and steady, and the hare is just too sure of himself. Consider the next problem as something that may have been the specific details of that story.

Trains in a tunnel

At 7 o’clock, a train enters a tunnel on the only to pass, go around, over or under one another

Track that runs through that tunnel. Another in the tunnel. However, it was possible for the

Train enters the exact same tunnel at 7 o’clock trains to make it to the other end of the tunnel

On the same day. There is no way for the trains untouched. How can that be?

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The Problem: The tortoise and the hare are both poised at the starting line of a 1-mile race. The tortoise can muster up a full 1-mile-per-hour speed, and the hare boasts a hopping speed of 8-miles-per-hour. The starter’s gun sounds, and both take off at their top speed. After one minute, the hare decides he has time to take a nap and snoozes for the next 54 minutes. He wakes up and makes a dash for the finish line. How long does it take him to catch up to the tortoise?

^VLAAf The distance that both the tortoise and the hare travel are the precise

Moment that the hare catches up to the tortoise. The rates are 1-mile-per-hour for the tortoise and 8-miles-per-hour for the hare. The tortoise moves along for T Hours, and the hare has T Minus 54 minutes (which has to be

54 9

Changed to miles per hour) so it’s T — = T — = T — 0.9 hours. Setting the two distances equal to one another and solving,

1t = 8 (T — 0.9) T = 8t — 7.2 7.2 = 7t

T = 7^ . L03

So the distances are equal and the hare catches up in a little more than one hour. But that’s too late. The tortoise crossed the finish line after one hour, and the hare hadn’t caught up to him yet, so the tortoise wins, yet again.

Speeding things up a bit

When you want to catch up with your older brother, you need to move faster than he’s moving, if he left before you.

The Problem: Don left home with his fishing gear and headed for his favorite spot at 6 a. m. Don bicycles at 6 mph. Don’s younger brother, Doug, left home at 6:30 and caught up with Don at 6:45 a. m.. How fast did Doug have to travel to catch up to Don at that time?

^VLA* The distance traveled by the brothers is the same, so set the products of the rates and respective times equal to one another. Don bicycled at 6 mph for 45 minutes. Doug traveled for just 15 minutes. Changing 45 minutes to 0.75 hour and 15 minutes to 0.25 hour, then the only unknown is Doug’s rate of speed, which is represented by r. The equation 6(0.75) = r(0.25) sets the two distances equal to one another. Simplifying on the left, you get 4.5 = 0.25r. Dividing each side by 0.25, you get that R = 18 mph. Doug must be riding a bike or driving.

The Problem: Carole left Tampa one hour after Warren. Carole caught up to Warren 200 miles from Tampa, because she drove at a rate of speed that’s 125 percent Warren’s speed. How fast did Carole and Warren drive?

^VLA/V Both Carole and Warren drove 200 miles. Let R Represent Warren’s speed and T Represent how long Warren drove to make that 200 miles. For Warren, you write the equation 200 = Rt. Carole drove the same 200 miles, but she drove faster and for one hour less than Warren. For Carole, you write the equation 200 = (1.25r)(t – 1). Going back to Warren’s equation, solve for T In terms of the 200 and r, and replace the T In Carole’s equation with that expression.

200 = Rt, t = 200 200 = (1.25r)(T — 1)

200 = (1.25r)(200 —

Next, distribute the 1.25r over the terms in the parentheses and solve for R.

200 = 1.25/X 200 — 1.25r X 1 200 = 250 — 1.25r

1.25R = 50

R = ^r°- = 40 1.25

Warren drove at 40 mph, so it took him 5 hours (200 40) to drive that 200 miles. Carole drove at 125 percent of Warren’s speed, so she drove at 50 mph. It took her four hours (200 50) to drive the same distance — one hour less than the time it took Warren.

Solving for the distance

The main element of the Distance = rate X Time Problems is the distance. You solve for rate or time when given the distance or given the fact that the distances traveled by the participants are equal. Just as important is finding out just how far people have traveled.

The Problem: Paula caught a bus to travel from school to home. Three hours later, her brother, Ken left school to go home driving his own car. If Ken drove 20 miles per hour faster than the bus, and arrived home at the same time as Paula, how far is it from school to home?

^VLA/V The distances are the same. You solve for the rate and time and then compute the distance. Letting R Represent the rate at which Paula is traveling on the bus, Ken is driving at the rate of R + 20 mph. The time that Paula traveled is T Hours, and Ken traveled T - 3 hours. Letting the two distances be the same, you get the equation Rt = (r + 20)(t – 3). Multiplying on the right, you get Rt = Rt -3r + 20t – 60. Subtracting Rt From each side and adding 60 to each side, the equation becomes 60 = 20t – 3r. It appears that there are many different times and rates that fit the solution as it’s given. Using the equation 60 = 20t – 3r you can try out some values for T And R. Some possibilities are shown in Table 16-1.

Several of the entries in the table are reasonable scenarios for Paula and Ken. To actually finish the problem, you need a little more information. Assume, for instance, that Ken drove 60 mph. That means that the bus Paula is riding on is driving at 40 mph. The equation now becomes 40t = 60(t – 3), which multiplies out to be 40t = 60t - 180. Simplifying, you get 180 = 20t Or T = 9. If Paula rode 9 hours at 40 mph, then the distance from school to home is 40 X 9 = 360 miles.

When you’re racing against someone bigger or older or faster, and she wants to make a contest of it, you can ask for a Head start. Applying this situation to a distance problem, you equate the distances by adding or subtracting the head start to make the finish come out the same. Getting a head start helps to even the playing field. It makes a race more of a contest and more interesting if the runners appear to have an equal chance of winning.

The Problem: The contestant from Kenya can run the 10,000-meter race at an average of 6 meters per second. The contestant from Ethiopia has a best time so far of 5.5 meters per second. How far back should the runner from Kenya start to have the expectation that they would cross the finish line at the same time if they both start at the same time?

In this problem, the distances aren’t really equal. You have to add on X Number of meters to represent the additional distance that the runner from Kenya must cover. The rates are also different, but the times will be the same, if they start at the same time and finish at thde same time. Take the distance formula, D = Rt And solve for T, Giving you T = —. Now set the time it takes the runner from Kenya equal to the time for the runner from Ethiopia. Then change the times to distances and rates.

TK = TE

~T~ = R

K e

Replace the denominators with the respective rates, and let the distances be 10,000 for the Ethiopian runner and 10,000 + X For the Kenyan runner. Then solve for X By cross-multiplying.

10,000 + X 10,000

- =

6 5.5 5.5 (10,000 + X) = 6 (10,000) 55,000 + 5.5x = 60,000

5.5X= 5,000

5,000 X = R r . 909.09

The runner from Kenya will have to start over 900 meters behind the other runner. And that’s assuming that she can run her usual pace for an extra 900 meters.

Working It Out with Work Problems

Work problems usually involve two or more people pitching in together to make a lighter load for everyone involved. Different people work at different rates of speed, so some people accomplish more of the total job than others.

Here are the overriding principals or procedures to use in doing these problems:

E* Let X Represent the amount of time needed to do the whole job.

E* Let 3, 4, ••• represent how much can be accomplished in One day By the person who can do the whole thing in 2, 3, 4, . . . days, respectively (other time units also apply).

E* Let X, ^3, xx, • • • represent how much of the Whole job Is accomplished by the person who can do the job in 2, 3, 4, . . . days, respectively.

E Add up all the fractions with X In the numerator and set them equal to the number 1 for the whole job (or a fraction for part of the job).

A traditional problem is that two or more people get together to paint a house. You assume that everyone has a paint brush, paint, ladder, and any other supplies needed to do the job. Working together, they reduce the amount of time necessary to complete the whole job.

The Problem: Tom, Dick, and Harry arrive early one morning at the job site and get ready to paint a huge, old, Victorian mansion. Tom, working by himself, could paint the whole house in 14 days. It would take Dick 10 days to do the job by himself. And Harry could do the job in 8 days. How long does it take for the three men to do the job working together?

Let X Represent the amount of time needed to do the whole job. Then Tom

Will do tt of the job, Dick will do ttt of the job, and Harry will do X Of the 14 10 8

Job. Add the fractions together and set them equal to 1.

Xc J Xc J Xc_ 1

14 10 8

Solve for X By first multiplying both sides of the equation by 280 and then simplifying.

X X 28020 + x X 28028 + X X 28035 = 1 X 280 yl 10 8

20x + 28x + 35x = 280

83X= 280

280 83

It will take the men not quite three and a half days to do the job by working together.

In some instances, though, the whole crew doesn’t show up at the same time.

The Problem: A three-man crew can harvest the field in six hours, while a four-man crew can harvest the field in four hours. If the three-man crew worked for one hour and then were joined by the fourth man, how long will it take the four-man crew to finish the job? How long does it take from start to finish to do the whole job?

^VLA/V First, determine how much is accomplished by the three-man crew before the fourth man shows up. Then determine how long it’ll take to finish up the job. If the three-man crew can do the harvesting in six hours, then in one hour,

They’ve done – i of the job and have 5 left to finish. Let X Represent how long it’ll take to finish the job, divide by 4 (the amount of time it takes the four-man crew to do the whole job) and set X Equal to the fraction of the job that’s left. Solve for X By cross-multiplying.

X = 5 4 = 6

6X= 20

20 O 1 63

It’ll take another 3 hours and 20 minutes to finish the job. Add that to the hour spent by the three-man crew, and the whole harvesting process took 4 hours and 20 minutes.

What if someone leaves before finishing the job? After all, people get tired or have other commitments. Have you ever been left to finish up a project that many other people had started? I’ll at least make this next job something fun to do.

The Problem: Sarah, Sue, and Sybil are making chocolate-chip cookies for the annual club bake sale. Working alone, it would take Sarah 8 hours to do all the baking. Sue could do the whole job in 10 hours, and it would take Sybil 12 hours by herself. They all started working early in the morning. But, after 2 hours, Sybil said that she had to leave for an appointment and wouldn’t be back. One hour after that, Sue got tired of listening to Sarah’s griping and left. How long did it take Sarah to finish up the job by herself, after the other two left?

£,?LAiV First, figure out how much of the job got accomplished during the first two hours, before Sybil left. If Sarah can do the job alone in 8 hours, then she did

2 (\ J = 2 = t in that two hours. Sue can do the job alone in 10 hours, so, in

That first two hours, she did 21 tq j = Tq = 5 of the job. And Sybil did

2 C 1j J = 12 = T in that first two hours. Add the three fractions together —

T + T + T = 15 + 12 + 10 = 37 — and you see that they’re over half finished

4 5 6 60 60 J J

With the job in the first two hours.

Next, determine how much more is accomplished in the next hour, with just

Sarah and Sue working. Add – i + ttt = 5 4 = -777 To get how much of the job 0 8 10 40 40 0 ‘

Is done by the two working together for an hour. Add the amount from the

First two hours to this amount, and you get the total amount of the job that’s

Been accomplished so far: 37 + -777 = 74 +a27 = t°7T. To determine how r 60 40 120 120

Much time it’ll take Sarah to finish the job, first subtract what’s been done

From 1, and then set that equal to X + 8.

1

101 = J9_ 120 120 X 19

- = -

8 120 X 19

= -~r—

8 T20i5

15X = 19

19 = i_4_ 15 t15

X

It’ll take Sarah another 1 hour and 16 minutes (changing the fractional remainder to minutes) to finish up the job by herself.

Incoming and Outgoing

Filling and draining pools and tanks are just other variations on work problems. When you have more than one water pipe pumping water into a tank, it takes less time than one pipe doing the filling by itself. An added twist to these problems is that the tanks can be emptying, too. If your pool has a leak in it, then water is going out one hole at the same time it’s coming in a pipe.

The Problem: A backyard swimming pool is being filled by two different hoses. One hose can fill the pool in 10 hours, and it takes the other hose 14 hours to fill the pool. How long will it take for the two hoses to fill the pool if they’re turned on at the same time?

DfQ^L Let X Represent the amount of time it’ll take the two hoses, working together, to fill the pool. Then write two fractions, one with X Divided by 10 and the other with X Divided by 14 to represent how much of the whole job each hose can accomplish. Add the two fractions together, set the sum equal to 1, and solve for X.

X J X _1

10 14

X # 707 + Tt x 705 _ 1 X 70

7x + 5x _ 70 12x _ 70

70 35 5

12 6 6

It’ll take 5 hours and 50 minutes to fill the pool with the two hoses.

The Problem: A pool takes six hours to fill and eight hours to drain. The drain was accidentally left open for the first three hours while the pool was filling and then closed. How long did it take for the pool to be filled?

^jlVLA* In the first three hours, the intake was 3 _ 4, which is obtained by dividing Ffr-zOs. 6 2 3

3 by the 6 hours it takes to fill the pool. At the same time, the outgo was 3,

8

Dividing 3 by the 8 hours it takes to drain. Subtract the two fractions to get a

Net filling of 4 — 3 _ 3 — 3 _ 4, which is the fractional amount that the pool

28888

Is full right now. Subtract that fraction from 1 to get the amount still needed to be filled: 1 — – g – _ Lg.

Let X Represent the number of hours it now takes to complete the filling of the pool. Write the fraction dividing X By 6, set it equal to the fraction of the pool needed to be filled, and solve for X.

X_ = 7

6 = 8 8x = 42

X = -482 = 5-^ =

It took another 5 hours and 15 minutes to fill the pool after the drain was closed, so the total time was 8 hours and 15 minutes.

The Problem: In the tank of a water tower, the intake valve closes automatically when the tank is full and opens up again when 5 of the water is drained

Off. The intake fills the tank in 4 hours, and the outlet drains the tank in 12 hours. If the outlet is open continuously, then how long a time is it between two different instances when the tank is completely full?

^VLA* Start with the first instance that the tank is full. The intake valve closes, and only the outlet valve is working, emptying the tank. You need to determine

How long it takes for the outlet valve to empty the tank by 5, leaving it 5 full.

Divide X, The amount of time it’ll take to lower the amount in the tank, by 12.

X 3

— = —

12 5

5X = 36

X = ~5~ = ^ 5

It takes 7 hours and 12 minutes for the amount of water in the tank to reach the level at which the intake valve switches on. Now you determine how long it takes to fill the tank again. Let X Represent the total amount of time needed. Divide X By 4 for the intake value and subtract the fraction formed by dividing

X By 12 for the outlet. Set the difference equal to 5, the amount of the tank

That needs to be filled. Solve for X By first multiplying each term by 60, the common denominator.

X

601

10X = 36

36 = 33 10 = 3 5

4

It’ll take another 3 hours and 36 minutes to fill the tank. Add the 7 hours and 12 minutes to get the tank to the level where the intake kicks in, and add the 3 hours and 36 minutes. It’s a total of 10 hours and 48 minutes between times that the tank is full.

Chapter 17

In This Chapter

^ Finding out what massage therapy is all about

^ Understanding how massage works

^ Exploring different types of massage therapy

^ Discovering what massage can be good for

^ Knowing what to expect in a typical massage treatment

^ Knowing how to find a safe and effective massage therapist

Assage is one of the oldest forms of therapy, having been practised since time immemorial. Touch is reassuring, relaxing, and healing, and even essential – in early life, babies and infants deprived of touch fail to thrive.

The touch of a mother’s hand can soothe a crying infant or ease a child’s pain; a neck and shoulder rub squeezed into a lunch hour can improve an office worker’s performance and well-being; a massage from a sports therapist can ease an athlete’s cramp; and self-massage of temples or belly can ease headache or abdominal pain. These are just some examples of how anyone can give and receive massage and benefit from it.

In this chapter I introduce you to a whole host of different types of professional massage. You’ll look at old and new massage therapies from both East and West and their benefits. You’ll also explore just what it is about massage that makes you feel soooooo good!

I also tell you a bit about research that supports the use of massage and give you some tips on how to find a safe and effective massage therapist. At the end of the chapter I show you a quick massage that you can give yourself at any time, especially if you’re short of time or money.

Finding Out about Massage

Massage is the use of different types of touch, pressure, and movement on the skin and underlying tissues to release tension, pain, and blockage and to help you feel good. The word Massage Is thought to have come from either the Greek word Masso, Which means ‘to knead’, or the Arabic Mas’h, Meaning ‘to touch, feel, or handle’. The ancient Greeks, Egyptians, Romans, and other ancient civilisations are all known to have enjoyed massage.

Every culture and medical system has one or more different forms of massage, and massage techniques have also been incorporated into many different therapies used today, including osteopathy and chiropractic. Modern massage therapists may specialise in one type of massage or may have been trained in several and then use them individually or in combination.

Massage is believed to provide a range of benefits including increased circulation, improved immune function, relaxation of muscles, and relief from pain, inflammation, and fluid retention, as well as enhanced self-esteem and well-being.

Massage is a hugely popular therapy and is utilised in beauty salons, spas, health centres, hospitals, offices, schools, sports centres and gyms, homes for the elderly, and baby units, as well as, of course, in the home.

A (very) brief history of massage

Massage features in ancient Chinese scrolls that date back to 400 BC and in papyrus scrolls of the ancient Egyptians. The great ancient Greek physician Hippocrates recommended massage, and Julius Caesar and his Roman colleagues had it regularly, too.

Massage ability can even be life saving! The great French Renaissance doctor, Ambroise Pare, was a hearty barber-surgeon who became famous as an army doctor for devising humane and natural methods to save soldiers’ lives. For example, he used eggs, oil of roses, and turpentine to treat amputation stumps and massage and physical therapy to rehabilitate

Injured soldiers. On one occasion he was captured by enemy soldiers and was just about to be executed when he was recognised. Because of his great healing skills he was spared and went on to write-up his healing techniques in a series of books and became personal physician to a succession of kings at the French royal court.

Massage continued to flourish down the centuries and in the 16th-century became popular in the French Court on the recommendation of the extraordinary royal physician, Ambroise Pare, who favoured natural healing methods. In the late-18th and early-19th centuries, massage came into its own as a standalone therapy due largely to the work of a Swede, Per Henrik Ling (1776-1839).

Ling was a gymnast and fencer who studied medicine and created a system of medical gymnastics that was later taught with government and medical approval at the Royal Gymnastic Central Institute in Stockholm.

The massage elements of Ling’s system, based on a sound understanding of anatomy and physiology, were taken up by a Dutch practitioner, Johan Georg Mezger, who coined the French names for the different moves (see ‘Exploring Different Types of Massage’ later in this chapter to find out what these moves are). This system of massage, known as Therapeutic massage Or Swedish massage (except in Sweden!) is now practised around the world and has influenced many subsequent massage systems.

Massage continued to be popular in the 19th and 20th centuries with the development of physiotherapy, but fell out of favour as pharmacology and instrumentation (the use of mechanical devices for skin stimulation and therapy) came into vogue. Massage also gained a bad reputation by often being used as a misnomer for sexual services.

Nowadays, however, extensive research has helped to change people’s perception of massage and it is now seen as a useful therapy as well as a form of relaxation and pleasure.

The range of massage therapies used today is very wide. They vary in terms of their origins (both East and West), their techniques (depth of pressure, type of massage movements), and their focus (physical effects, such as the release of muscular tension, or more subtle aspects, such as improving the flow of ‘vital energy’ in the body).

Grasping the idea behind massage

Massage has a direct effect on the skin, muscles, nerves, blood vessels, and lymph system (a network of vessels that transport a nearly colourless cellular fluid that plays a role in the immune system) and can also affect the functioning of the internal organs.

These effects are due to the mechanical action of massage and also the reflex action of the body. The Mechanical action Is the actual pressure and stretching movements of massage, which help to stimulate the release of built up acids and other toxins and to loosen up stiff joints. The Reflex action Is the body’s response, which can trigger an effect in another part of the body.

Essentially, the massage stimulates skin receptors that relay messages to the brain via the nervous system. The brain in turn sends messages back to the area being massaged causing muscle relaxation, blood vessel dilation, and improved blood circulation.

Production of feel-good chemicals – the endorphins – is also triggered. These endorphins provide pain relief and also increase the sense of well-being – which is why people report feeling reassured, soothed, and relaxed after massage.

The benefits of massage

The effects of massage can be physical, psychological, emotional, and even spiritual. Physical benefits may include the following:

Improved circulation

Release of tension, stiffness, cramps, and pain Improved mobility and range of movement Breakdown of scar tissue Better muscle tone and flexibility Better sleep

Increased energy and vitality I Improved immune function I Lowered blood pressure

Improved removal of waste matter from the body I Increased supply of oxygen and nutrients to the tissues I Faster healing

Psycho/emotional benefits can include the following:

I Increased sense of well-being

I Greater self-confidence and self-esteem

I Improved concentration, memory, and creativity

I Less stress, anxiety, and irritability

I Greater sense of calm and relaxation

People also sometimes report feelings of bliss and ‘oneness’ or spiritual attunement during massage.

Massage today

Today, massage flourishes in most Western countries but none have a single governing body or formal regulatory system. This situation means that qualifications and standards can vary quite considerably.

In the UK, a new National Register for Massage Therapists was established in 2004 by the General Council for Massage Therapy (GCMT; Www. gcmt. org. uk). Its members have all completed approved massage training courses, are bound by a code of conduct, and carry professional indemnity insurance. However, this council still only represents a small number of the many massage associations that currently exist.

Similar situations exist in other countries (see ‘Finding a Massage Therapist’ further on in this chapter).

Evidence that it works

Massage has been shown to be effective for a range of conditions including: back and other types of pain, fibromyalgia (chronic ache and pain), fatigue, stress, blood sugar control, insomnia, anxiety, and attention deficit and hyperactivity disorder (ADHD), to name but a few. This therapy has also been shown to improve your golf swing!

Additionally, massage has been shown to be effective in the treatment of premature babies, in the care of the elderly, and as an aid for recovery after surgery and during cancer treatment.

For examples of massage research take a look at the research pages of the General Council for Massage Therapy on Www. gcmt. org. uk/research. asp. Other studies can be found on Www. internethealthlibrary. com/ Therapies/MassageTherapy-Research. htm; the NHS Complementary and Alternative Medicine Specialist Library (Www. library. nhs. uk/cam); the Bastyr University Research database on Www. bastyr. edu/research; or the PubMed database on Www. nlm. nih. gov/nccam/camonpubmed. html.

Exploring Different Types of Massage

Many different types of massage exist. These can be divided into Western forms (mainly Swedish, Danish, and Norwegian massage therapies), Japanese forms (Anma, Shiatsu, and Amatsu), Chinese forms (tui na and acupressure), and

Indian forms (Ayurvedic massage, Indian Head massage, Chavutti Thirumal, and so on). Thai, Tibetan, Mongolian, Indonesian, Hawaiian, and other forms of massage are also practised, as well as specialist types of massage including baby massage, hot stone massage, and sports massage.

Here’s an A-to-Z of some of the most popular types of massage therapy:

U Acupressure: Originated in ancient China and uses finger pressure applied to acupuncture points on the skin to regulate the flow of Qi (vital energy) in the acupuncture meridians. Acupressure techniques are a part of many other therapies, including Shiatsu, tui na, Shen Tao, and Jin Shin Do.

Uu Amatsu: Originated in Japan this is a modern day combination of anma massage, Seitai (bone adjustment), Shinden-jutsu (balancing of the ligaments and soft-tissue massage), and Kenkujutsu (Japanese cranial therapy). This therapy has recently been introduced to the West. For more, see Www. amatsu. info.

U Anma: The oldest form of massage in Japan. Uses the thumbs, fingers, knuckles, elbows, knees, and feet to press, stroke, stretch, and percuss the skin. This massage is performed through clothing and no oils are used.

U Aromatherapy: Combines massage with the use of essential oils extracted from plants, which are inhaled as well as absorbed through the skin. For more about this therapy, see Chapter 19.

U Ayurvedic massage: Traditional Indian medicine, known as Ayurveda, employs several types of massage. Marma massage involves the application of pressure to a range of special Marma Points on the body, similar to the acupoints of acupuncture. Other types of massage are selected according to the person’s Dosha Or ‘vital energy’ type and use different oils, pressure, friction techniques, and speeds. Specialist techniques include Chavutti Thirumal, a South Indian massage done with the feet and toes by a therapist suspended on ropes, and Indian Head massage, Also known as Champissage, Which involves scalp, neck, face, ears, and shoulders massage. For more, see Chapter 5.

U Baby massage: Incorporates gentle massage strokes and stretches to stimulate the baby’s immune system and aid digestion and relaxation.

U Biodynamic massage: Created by Norwegian physiotherapist and psychologist Gerda Boyesen, this massage therapy is designed to release physical and energetic blockages in the muscles and abdomen. For more, contact the Association of Holistic Biodynamic Massage Therapists (AHBMT) at Www. ahbmt. org.

U Chua Ka: An ancient form of Mongolian massage using a stick, called a Ka, And the hands to massage deep into the muscles and release tension and fear.

I had the great privilege to study Shiatsu with Masunaga’s successor, Suzuki Sensei, when I lived in Tokyo. He told us many stories about Masunaga and his amazing innovations. Masunaga read extremely widely but also let his hands and the bodies of his patients be his teachers. He spent countless hours trying out techniques and carefully palpating the body to observe and test its reactions.

The acupuncture meridian system had remained unchanged for thousands of years yet Masunaga redrew it! He followed the pathways of the arm meridians and extended them throughout the

Body. I was absolutely amazed by this extension of the pathways and found, on palpation and working with Masunaga’s stretches, that they made perfect sense. I also found that his system of diagnosing and treating through the abdomen was extraordinarily effective as well as his system of self-help meridian stretches. Masunaga’s marvellous techniques and exercises have been made available to all in the excellent book, Meridian Exercises: Oriental Way to Health and L/itality (Japan Publications, 1997) translated by Stephen Brown.

U Deep-tissue massage: Uses deep finger pressure and slow movements to break down scar tissue and compacted muscle fibres to release toxins, and ease tension and pain.

U Do-In: A traditional Japanese system for personal and spiritual development combining self-massage, acupressure, and shiatsu stretches with macrobiotic diet, breathing exercises, and meditation.

U Hot stone massage: Warm stones are placed on the body to increase circulation and relax muscles, or cool stones are used to reduce inflammation and swelling. For more information, see Www. lastonetherapy. com.

U Hydrotherm massage: This massage is performed while you lie on a mattress filled with warm water.

U Indonesian massage: This deep massage uses the thumbs to penetrate deep into the muscles and soft tissue.

U Jin Shin Do: Meaning ‘the way of the compassionate spirit’, this is a modern day synthesis of acupressure, Qi gong exercises, and psychology, developed by Iona Teeguarden in the US. For more, see

Www. jinshindo. org.

U Kahuna: Sometimes called Lomi Lomi, This Hawaiian form of deep-tissue massage uses long, flowing strokes, rhythmical pressure and oils over the whole body.

IU Manual lymphatic drainage: Danish physician Dr Emil Vodder developed this technique in the 1930s, using gentle touch and rhythmical movements to improve the flow of lymph (colourless fluid that surrounds the tissues and circulates via lymph vessels). J. R. Casley-Smith combined lymphatic drainage with skin care, compression bandaging, and special exercises to create complex physical therapy (CPT); while Australian Grace Halliday devised deep lymphatic therapy (DLT), by combining systematic lymphatic massage with hot foments (applied steam heat). For more information, see Www. mlduk. org. uk.

IU Myofascial massage: A technique used in Rolfing (see Chapter 16) and sports massage (see below) involving compression and skin rolling to stretch the fascia (tissues surrounding the bones and muscles), relieve pain and injury and increase mobility.

U Neuromuscular therapy: Also known as trigger-point therapy or

Myotherapy, this involves concentrated thumb/finger pressure to trigger points – tender points that have become sensitive due to lack of flow of blood and nutrients.

U On-site massage therapy: This is brief massage taken into the workplace using a special portable chair, which you sit on and lean forward in while massage is applied to the head, neck, shoulders, back, arms, and hands.

U Pregnancy massage: Gentle massage techniques to improve blood flow and reduce pregnancy discomfort.

U Reflexology: The application of fingertip and thumb pressure to points on the soles of the feet believed to be connected to different parts and organs of the body via the nerve reflex system.

U Remedial massage: A form of soft tissue massage used to treat muscle and joint pain and injuries.

U Self-massage: Simple pressure point and kneading techniques that you can do yourself to release tension and improve circulation. (For an example, see the end of this chapter.)

U Shiatsu: Meaning Finger pressure, This Japanese therapy involves

Stretches and pressure from the thumbs, fingers, palms, elbows, knees, or feet while you lie on a padded mat, or Futon, On the floor.

Various styles of shiatsu have been developed in Japan and spread to the West. Namikoshi Shiatsu (sometimes called shiatsu massage) was created by Tokujiro Namikoshi in Japan in the 1920s, and developed from instinctive pressure point massage that he gave his rheumatic mother as a child to ease her pain. In the 1950s, he took this therapy to America and his work is now continued by his son Toru, who has emphasised the role of Western anatomy, physiology, and pathology.

Shizuto Masunaga developed Zen Shiatsu By incorporating traditional Chinese medicine theory of Yin And Yang (called In And Yo In Japanese – nip over to Chapters 4 and 7 for an explanation of these) and the concept of balancing deficiency (kyo) And excess (jitsu) In the meridian channels by

Means of shiatsu massage and stretches. He also devised a unique form of abdominal diagnosis and treatment called Hara Massage.

Another popular style is Tsubo therapy Developed by Katsusuke Serizawa. This style focuses on stimulation of the Tsubo, Or acupoints, using massage, moxa (heat treatment), or electrical stimulation.

For more information on shiatsu and shiatsu practitioners, check out

Www. shiatsu. org.

U Sports massage: A combination of remedial, deep-tissue, and Swedish massage techniques used to relieve muscle stiffness and pain, improve athletes’ performance and aid recovery from injury.

U Thai massage: Incorporates Ayurvedic and Chinese massage and uses pressure point therapy, muscle stretching, and firm compression techniques to release tension and relax the body.

IU Therapeutic massage (Swedish massage): Developed by Per Henrik Ling in Sweden at the end of the 19th-century, and systematised by Dutchman Johan Georg Mezger, this influential type of massage employs five basic moves to stimulate the tissues and ease muscle tension:

• Petrissage: This technique involves kneading and squeezing the soft tissues (the tissues around the bones and organs of the body) and both the superficial and deep muscles of the body

• Friction and compression: These rubbing and holding techniques are designed to break down build-ups of scar tissue and to relax the muscles

• Tapotement: These are rhythmical, tapping movements, usually made with the edge of the hand or the heel of the palm, designed to increase blood circulation

• Vibration: These are rhythmical, vibrational movements designed to release tension and stimulate circulation

Swedish massage is usually performed without clothing and on a massage couch using oils and lotions. Most of the moves are directed towards the heart.

U Tibetan massage: This involves pressure to therapeutic points on the body as well as kneading, rubbing, and tapping techniques to relax the body and ease tension. Sesame, or other, oil may be used to warm the tissues and ease the massage moves (for more on Tibetan medicine, take a look at Chapter 6).

IU Tui na: Meaning ‘push and grasp’, tui na is an ancient form of Chinese massage that uses fingers, hands, arms, elbows, and knees to vigorously rub, knead, and roll the skin and tissues. This massage is designed to release energetic blockage in the acupuncture meridians and to release muscular tension.

Effleurage: This massage is designed to stretch and relax the superficial muscles

I once had a Thai massage in the Temple of Wat Instead of being relaxing, the massage was

Pho in Bangkok, Thailand, which houses the incredibly invigorating! I remember being pulled

Longest reclining gold Buddha in the world. into all sorts of positions and walked all over. At

Instead of the privacy you might expect in the the end of the massage I felt as if I’d been

West, the massage room consisted (at that beaten up but my level of energy was extraor-

Time) of an open hall with row upon row of dinary. I felt as if I could run round that long,

Simple beds on which the Thai masseurs gold Buddha all night! worked on lots of people simultaneously.

Understanding Massage Diagnosis

Massage therapists use their sense of touch, and palpation of the skin, to identify areas of pain, tension, inflammation, or water retention and to determine the condition of the skin tissues.

Shiatsu therapists also use the acupuncture meridian lines and acupoints to gauge information about the functioning of each of the internal organs (see Chapter 9 on Acupuncture for more about these), while reflexologists use reflex areas on the feet to identify possible problems with individual organs or body parts.

Massage therapists do not claim to make medical diagnoses. If you’re concerned about a medical condition, consult your doctor.

Finding Out about Massage Treatment

Massage is best performed in a relaxed, peaceful environment by a practitioner, friend, or partner that you trust and feel completely comfortable with. Sometimes relaxing music, low lighting, or pleasant aromas from aromatherapy or incense burners may be used to add to the relaxing effect of the treatment.

Discovering whom and what massage is good for

Massage is suitable for anyone and may be used therapeutically to treat different ailments or used simply for pleasure and relaxation.

The types of conditions most often treated by massage therapists include back pain, headaches, arthritis, fatigue problems, Repetitive Strain Injuries (RSI), sports injuries, asthma, strains and sprains, digestive problems, insomnia, and stress.

When not to use massage

Don’t use massage if you:

U Have an infectious skin condition (such as impetigo) U Are suffering from flu or high fever U Have sunburn

IU Feel extremely unwell, or debilitated from some disease U Are under the influence of alcohol or recreational drugs

Special care must also be taken in the case of small infants, pregnant women, and the elderly, and also for those suffering from high blood pressure, heart conditions, cancer, asthma, epilepsy, diabetes, or osteoporosis. Massage needs to be avoided at the site of scar tissue, varicose veins, sprains and fractures, cuts, verrucas, eczema, psoriasis, and so on.

If you’re taking pharmaceutical drugs, such as for high blood pressure, epilepsy, diabetes, or asthma, make sure to inform your massage therapist.

What to Expect in a Typical Consultation

A massage treatment usually begins with some questions about general health and any problem areas of tension or pain in the body. You may then be asked to disrobe.

Many massage therapies are performed directly on the skin so you may be asked to undress to underwear and then be covered with towels. The room is usually kept warm to aid relaxation. Some massage therapies, such as shiatsu and Thai massage, may be performed through clothing. Wearing loose, cotton clothing for these types of treatment is advisable.

Massage may involve the use of oils, lotions, or talcum powder to ease friction on the skin (as in Swedish massage and Ayurvedic massage), or may be performed ‘dry’ such as in shiatsu massage.

You may be asked to lie on a treatment couch, sit on a massage stool, or lie on a mattress on the floor, depending on the type of massage you’re going to receive.

The massage usually begins gently and then may become more vigorous depending on the style. Massage is usually very relaxing but some of the deep-tissue techniques, for example those used in Thai massage, may feel a bit tender or even mildly painful, depending on the area and type of tissues being worked on. If you feel discomfort, let your therapist know.

You may want to have your eyes open or closed during the massage and to talk or to be quiet. Some people feel so relaxed they even fall asleep during their massage!

Stretching exercises and dietary or lifestyle advice may also be part of the therapy.

To get the best results from your massage:

I Relax as much as possible. I Drink plenty of water before and afterwards.

I Avoid stimulants such as coffee, tea, sugar, or cigarettes and also alcohol or recreational drugs for several hours beforehand.

I Avoid heavy meals prior to treatment.

I Get plenty of rest afterwards.

After the massage

After the massage is over you may feel tired or energetic, calm or emotional, as the massage can release deep-seated feelings. Some people experience mild muscle ache but this usually passes quickly. Finding that you need to go to the toilet (urination and/or stools) more often initially is normal because massage can stimulate the removal of waste products.

Duration and frequency

Massage treatments can last anything from 15 minutes (on-site massage) to 2 hours (Kahuna massage) but typically last around 60 to 90 minutes. Repeated massages, either daily or a few days or a week apart, may be advised in case of injury or illness and then spaced out. Therapeutic massages for relaxation and pleasure can be taken anytime.

Knowing Whether Your Massage Treatment Is Working

You may feel tired or slightly aching after massage but this passes quickly and you’ll soon feel the benefits of increased relaxation, circulation, and vitality.

I If you experience a marked worsening of your symptoms, contact your massage therapist for advice.

IU Ask your massage therapist what sort of health improvements you can realistically expect and over what sort of timescale.

I For best results, carefully follow the exercise and lifestyle advice given to you by your massage therapist.

I If you have no improvement after a course of treatment, you may want to consider another form of therapy. Discuss this situation with your practitioner.

Common Questions about Massage Treatment

Here are some questions that I’m often asked about massage:

IU Do I have to be naked? No, not necessarily. Take a look at the different types of massage mentioned earlier on in this chapter and choose one that allows you to keep your clothes on if you feel self-conscious.

I Will I feel embarrassed? Normally, YOur massage therapist will help you feel comfortable by enabling you to disrobe in privacy and keeping you covered with towels when possible during the massage. As an experienced health professional, your therapist will be focused on giving you the greatest therapeutic benefit from your massage, rather than on what your body looks like.

IU What does massage feel like? Pretty relaxing probably, blissful maybe, and tender perhaps, depending on the type of massage.

I How do I choose which type to have? Take a look at the main types of massage listed earlier in this chapter, see which tickles your fancy and give it a try! Things to consider include whether you’re dressed/undressed; full body or specific body part; environment (quiet, individual room, or communal setting); technique (relaxing or invigorating).

Finding a Good Massage Therapist

Massage therapists are not fully regulated in the UK, US, Canada, Australia, or New Zealand, so anyone can call themselves a ‘massage therapist’. Check that your practitioner is a member of a professional body and has had a thorough training at a reputable institution.

In the UK, many massage therapists are members of associations that are part of the General Council for Massage Therapy (GCMT), which maintains a practitioner register (Www. gcmt. org. uk). Another register can be found on

Www. massagetherapy. co. uk.

In the US, numerous different massage associations exist, many of which represent a particular type of massage only. Many of them are listed at Www. thebodyworker. com/associations_list. htm. One of the most well-established is the American Massage Therapy Association (www. amtamassage. org), which maintains a list of practitioners.

Following are some massage therapist associations in other countries:

I Australia: The Massage Association of Australia (Www. maa. org. au) or the Association of Massage Therapists Ltd (Www. amt-ltd. org. au)

I Canada: The Association of Massage Therapists and Wholistic

Practitioners (Www. amtwp. org) or the Canadian Massage Therapist Alliance (Www. cmta. ca)

I New Zealand: The Therapeutic Massage Association (TMA) and the Massage Institute of New Zealand (MINZI) have joined forces and, from April 2007, will become a new unified body called Massage New Zealand (MNZ). More details on Www. tmanz. org. nz

Finally, here are a few other ideas for finding a massage therapist:

I Ask friends, family, and colleagues for personal recommendations.

I Many sports and leisure clubs offer massage treatment.

I Check with local complementary medicine and alternative therapy clinics and magazines.

I Some beauty salons offer therapeutic massage, aromatherapy, and so on. I Most health farms and spas offer massage.

I Massage schools may have teaching clinics with reduced fees or can refer you to graduates. One of the most established schools in the UK is the Clare Maxwell-Hudson School of Massage (Www. cmhmassage. co. uk).

Questions to ask your massage therapist

You may want to ask your massage therapist about the following:

I Qualifications: Most practitioners are happy to give details of their training and qualifications and membership of a professional body. If you have any doubt as to their validity, check the qualifications with their respective professional body.

I Insurance: If your practitioner is a member of a professional register they’ll normally be required to have appropriate indemnity insurance.

I Experience: Ask your practitioner about their experience and familiarity with your particular health condition.

I Treatment: Ask about the likely frequency and duration of treatment and the cost involved.

Counting the cost of massage

Massage costs from Ј15 to Ј90 depending on the duration and type of massage. Massage treatment is very rarely available on the NHS or covered by private health insurance.

Some practitioners offer concessions for retired persons or those on benefits. Ask your practitioner for details.

Ensuring satisfaction

If you’re dissatisfied with your treatment, first talk things over with your practitioner.

If you think that the practitioner has been negligent or unethical in any way, contact their professional association or registering body, which should have a formal complaints procedure.

Helping Yourself with Massage

Self-massage can be a great way to relieve neck and shoulder tension.

1. Support your right elbow with your left hand and place your right hand over your left shoulder.

2. Grasp the flesh close to your neck and squeeze it firmly. Hold for a few seconds, then release.

3. Repeat this squeeze-release movement three times. Move the hand down slightly towards the shoulder and repeat the move again three times.

4. Move your hand down over your shoulder itself and again repeat the squeeze-release movement three times.

5. Swap your hands over and repeat this on the opposite side of the body.

Remember to breathe freely during the movements. At the end, your neck and shoulders feel tingling and relaxed.

This is a great technique to use when you’ve been typing for hours. I used it a lot during the writing of this book!

Part V