Exercise 38 Page 72

We are given that the speed limit of the boat pulling a beginner skier is 18 miles per hour. This means that they have a speed r less than 18 miles per hour. r<18 In order to find the distance traveled we can use a variation of the distance formula, d=rt. d=rt ⇔ r=d/tKnowing this, we can write an inequality for d. r<18 ⇒ d/t<18 We are also given that the practice time is 45 minutes. We need to rewrite either the speed limit or the practice time so that they both have the same time units. It is easier to convert 45 minutes to hours using a conversion factor. 1h/60min Let's do it!

45min*1h/60min

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Simplify

MoveLeftFacToNum

a*b/c= a* b/c

45min* 1h/60min

CrossCommonFac

Cross out common factors

45 min* 1h/60 min

SimpQuot

Simplify quotient

45h/60

ReduceFrac

a/b=.a /15./.b /15.

3h/4

MovePartNumRight

a* b/c=a/c* b

3/4h

Next, we will substitute this value for t in our inequality. d/34<18 Finally, we can solve this inequality to find the possible distances a beginner skier can travel.

d/34<18

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Solve for d

DivByFracD

a/b/c= a * c/b

4d/3<18

MultIneq

LHS* 3 < RHS * 3

4d/3 * 3 < 54

a/c* b =a * b/c

4d*3/3 < 54

QuotOne

a/a=1

4d < 54

DivIneq

.LHS /4.<.RHS /4.

d < 54/4

ReduceFrac

a/b=.a /2./.b /2.

d < 27/2

CalcQuot

Calculate quotient

d < 13.5

Therefore, a beginner skier can only travel less than 18 miles in 45 minutes.