Beginning Algebra, 11th Edition

(c) At the 2008 Olympic Games, Australian swimmer Leisel Jones set an Olympic

record of 65.17 sec in the women’s 100-m breaststroke swimming event. (Source:

World Almanac and Book of Facts.) Find her rate.

We must find rate, given distance and time, using

Rate NOW TRY

100

65.17

= 1.53 m per sec (rounded)

d

r = Aort = rB.

d

t

144 CHAPTER 2 Linear Equations and Inequalities in One Variable

Distance

Time

Solving a Motion Problem

Two cars leave Iowa City, Iowa, at the same time and travel east on Interstate 80. One

travels at a constant rate of 55 mph. The other travels at a constant rate of 63 mph. In

how many hours will the distance between them be 24 mi?

Step 1 Readthe problem. We must find the time it will take for the distance

between the cars to be 24 mi.

Step 2 Assign a variable.We are looking for time.

Let t the number of hours until the distance between them is 24 mi.

The sketch in FIGURE 16shows what is happening in the problem.

To construct a table, we fill in the information given in the problem, using t

for the time traveled by each car. We multiply rate by time to get the

expressions for distances traveled.

=

EXAMPLE 6

IowaCity

Faster car

24 mi

Slower car

East

FIGURE 16

Rate Time Distance

Faster Car 63 t 63 t

Slower Car 55 t 55 t

The quantities 63tand 55trepresent the two

distances. The differencebetween the larger

distance and the smaller distance is 24 mi.

Step 3 Write an equation.

Step 4 Solve. Combine like terms.

Divide by 8.

Step 5 State the answer.It will take the cars 3 hr to be 24 mi apart.

Step 6 Check.After 3 hr, the faster car will have traveled and

the slower car will have traveled The difference is

189 - 165 = 24, as required. NOW TRY

55 * 3 =165 mi.

63 * 3 =189 mi

t= 3

8 t= 24

63 t- 55 t= 24

NOW TRY
EXERCISE 6
From a point on a straight
road, two bicyclists ride in the
same direction. One travels at
a rate of 18 mph, the other at a
rate of 20 mph. In how many
hours will they be 5 mi apart?

NOW TRY ANSWERS

5. 66.67 mph 6.2.5 hr

In motion problems, once we have filled in two pieces of information in each

row of the table, we can automatically fill in the third piece of information,

using the appropriate form of the distance formula. Then we set up the equation

based on our sketch and the information in the table.

PROBLEM-SOLVING HINT

NOW TRY
EXERCISE 5
It took a driver 6 hr to travel
from St. Louis to Fort Smith,
a distance of 400 mi. What
was the driver’s rate, to the
nearest hundredth?

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