Step 3 Write an equation.

12

x+ 3

=

8

x- 3

SECTION 7.7 Applications of Rational Expressions 469

The time downstream equals the time upstream,

so the two times from the table must be equal.

Step 4 Solve.

Multiply by the LCD,

Divide out the common factors.

Distributive property

Subtract 8xand add 36.

Divide by 4.

Step 5 State the answer.The rate of the boat in still water is 15 mph.

Step 6 Check.First we find the rate of the boat going downstream, which is

mph. Divide 12 mi by 18 mph to find the time.

The rate of the boat going upstream is mph. Divide 8 mi by

12 mph to find the time.

The time upstream equals the time downstream, as required.

NOW TRY

OBJECTIVE 3 Solve problems about work.Suppose that you can mow your

lawn in 4 hr. Then after 1 hr, you will have mowed of the lawn. After 2 hr, you will

have mowed , or , of the lawn, and so on. This idea is generalized as follows.^24 12

1

4

t=

d

r

=

8

12

=

2

3

hr

15 - 3 = 12

t=

d

r

=

12

18

=

2

3

hr

15 + 3 = 18

x= 15

4 x= 60

12 x- 36 = 8 x+ 24

121 x- 32 = 81 x+ 32

1 x+ 321 x- (^32 1) x+ 321 x- 32.

12

x+ 3

= 1 x+ 321 x- 32

8

x- 3

Rate of Work

If a job can be completed in tunits of time, then the rate of work is

job per unit of time.

1

t

PROBLEM-SOLVING HINT

Recall that the formula says that distance traveled is equal to rate of

travel multiplied by time traveled. Similarly, the fractional part of a job accom-

plished is equal to the rate of work multiplied by the time worked. In the lawn-

mowing example, after 3 hr, the fractional part of the job done is as follows.

Rate of Time Fractional part

work worked of job done

After 4 hr,^14 142 = 1 whole job has been done.

3

4

1

4

3 =

d=rt

⎩⎪⎨⎪⎧ ⎩⎪⎨⎪⎧ ⎩⎪⎪⎪⎨⎪⎪⎪⎧

NOW TRY
EXERCISE 2
In her small boat, Jennifer can
travel 12 mi downstream in
the same amount of time that
she can travel 4 mi upstream.
The rate of the current is
2 mph. Find the rate of
Jennifer’s boat in still water.

NOW TRY ANSWER
2.4 mph