Intermediate Algebra (11th edition)

SECTION 7.5 Applications of Rational Expressions 399

Traveling withthe current speeds the boat up, so the rate of the boat is

the sumof its rate in still water and the rate of the current — that is,

Thus, the rate of the boat againstthe current,

and the rate of the boat withthe current.

Because the time is the same going against the current as with the

current, find time in terms of distance and rate for each situation. Against

the current, the distance is 10 mi and the rate is

Time againstthe current

With the current, the distance is 15 mi and the rate is

t= Time withthe current

d

r

=

15

x+ 3

1 x+ 32 mph.

t=

d

r

=

10

x- 3

1 x- 32 mph.

x+ 3 =

x- 3 =

1 x+ 32 mph.

Distance Rate Time

Against

10

Current

With

15

Current

15

x+ 3

x+ 3

10

x- 3

x- 3

Times

are equal.

We summarize the

information in a table.

Step 3 Write an equation,using the fact that the times are equal.

Step 4 Solve.

Distributive property

Subtract 10x. Add 45.

15 =x Divide by 5.

75 = 5 x

10 x+ 30 = 15 x- 45

101 x+ 32 = 151 x- 32

1 x+ 321 x- 32 a

10

x- 3

b = 1 x+ 321 x- 32 a

15

x+ 3

b

10

x- 3

=

15

x+ 3

Multiply by the LCD,

1 x+ 321 x- 32.

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

Step 6 Checkthe answer: 1510 - 3 = 1515 + 3 is true. NOW TRY

Solving a Problem about Distance, Rate, and Time

At O’Hare International Airport in Chicago, Cheryl and Bill are walking to the gate

at the same rate to catch their flight to Akron, Ohio. Since Bill wants a window seat,

he steps onto the moving sidewalk and continues to walk while Cheryl uses the sta-

tionary sidewalk. If the sidewalk moves at 1 m per sec and Bill saves 50 sec covering

the 300-m distance, what is their walking rate?

Step 1 Readthe problem. We must find their walking rate.

Step 2 Assign a variable.Let xrepresent their walking rate in meters per second.

Thus, Cheryl travels at a rate of xmeters per second and Bill travels at a rate

of 1 x+ 12 meters per second.

EXAMPLE 7

NOW TRY
EXERCISE 6
A small fishing boat goes
36 mi against the current in a
river in the same time that it
goes 44 mi with the current.
If the rate of the boat in still
water is 20 mph, find the rate
of the current.

NOW TRY ANSWER

6. 2 mph