Intermediate Algebra (11th edition)

Solving a Motion Problem

A riverboat for tourists averages 12 mph in still water. It takes the boat 1 hr, 4 min to

go 6 mi upstream and return. Find the rate of the current.

Step 1 Readthe problem carefully.

Step 2 Assign a variable.Let the rate of the current.

The current slows down the boat when it is going upstream, so the rate of

the boat going upstream is its rate in still water lessthe rate of the current,

or mph. See FIGURE 1.

Similarly, the current speeds up the boat as it travels downstream, so its rate

downstream is mph. Thus,

the rate upstream in miles per hour,

and the rate downstream in miles per hour.

Step 3 Write an equation.We use the total time of 1 hr, 4 min written as a fraction.

Total time

The time upstream plus the time downstream equals hr.

Time upstream Time downstream Total time

Step 4 Solvethe equation. The LCD is

Multiply by the LCD.

Distributive property;

multiply.

Multiply.

Distributive property

Combine like terms.

Add 16x^2. Subtract 2160.

Divide by 16.

or Square root property

Step 5 State the answer.The current rate cannot be so the answer is 3 mph.

Step 6 Checkthat this value satisfies the original problem. NOW TRY

- 3,

x= 3 x=- 3

x^2 = 9

16 x^2 = 144

2160 = 2304 - 16 x^2

1080 + 90 x+ 1080 - 90 x= 2304 - 16 x^2

90112 +x 2 + 90112 - x 2 = 161144 - x^22

15112 +x 2 # 6 + 15112 - x 2 # 6 = 16112 - x 2112 +x 2

= 15112 - x 2112 + x 2 a

16

15

b

15112 - x 2112 +x 2 a

6

12 - x

+

6

12 +x

b

15112 - x 2112 +x 2.

16

15

=

6

12 +x

+

6

12 - x

+ =

16

15

1 +

4

60

= 1 +

1

15

=

16

15

hr

12 +x=

12 - x=

112 +x 2

112 - x 2

x=

EXAMPLE 2

SECTION 9.3 Equations Quadratic in Form 513

Current

Riverboat traveling

upstream—the current

slows it down.

FIGURE 1

Complete a table. Use the distance

formula, solved for time t,

t=dr ,to write expressions for t.

d=r t,

dr t

Upstream 6

Downstream 6 6

12 +x

12 +x

6

12 - x 12 - x

Times in hours

NOW TRY
EXERCISE 2
A small fishing boat averages
18 mph in still water. It takes
the boat hr to travel 8 mi
upstream and return. Find the
rate of the current.

9

10

NOW TRY ANSWER

2. 2 mph