Beginning Algebra, 11th Edition

OBJECTIVE 2 Solve problems about distance, rate, and time.Recall from

Chapter 2the following formulas relating distance, rate, and time. You may wish to

refer to Example 5in Section 2.7to review the basic use of these formulas.

468 CHAPTER 7 Rational Expressions and Applications

Distance, Rate, and Time Relationship

drt r

d

t

t

d

r

Solving a Problem about Distance, Rate, and Time

The Tickfaw River has a current of 3 mph. A motorboat takes as long to go 12 mi

downstream as to go 8 mi upstream. What is the rate of the boat in still water?

Step 1 Readthe problem again. We must find the rate (speed) of the boat in still

water.

Step 2 Assign a variable.Let x=the rate of the boat in still water.

EXAMPLE 2

Because the current pushes the boat

when the boat is going downstream, the

rate of the boat downstream will be the

sumof the rate of the boat and the rate of

the current, mph.

Because the current slows down the

boat when the boat is going upstream, the

boat’s rate going upstream is given

by the difference between the rate of

the boat and the rate of the current,

1 x- 32 mph. See FIGURE 1.

1 x+ 32

Fill in the times by using the

formula .t=dr

drt

Downstream 12

Upstream 8 x- 3

x+ 3

The time downstream is the distance divided by the rate.

Time downstream

The time upstream is that distance divided by that rate.

t= Time upstream

d

r

=

8

x- 3

t=

d

r

=

12

x+ 3

Times are equal.

d r t

Downstream 12

Upstream 8 x- (^3) x^8 - 3
12
x+ (^3) x+ 3
This information is summarized in the following table.
Downstream
(with the
current)
Upstream
(against
the current)
x – 3
x + 3
FIGURE 1
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