Beginning Algebra, 11th Edition

41.One pipe can fill a swimming pool in 6 hr,

and another pipe can do it in 9 hr. How long

will it take the two pipes working together to

fill the pool full?

42.An inlet pipe can fill a swimming pool in

9 hr, and an outlet pipe can empty the pool in

12 hr. Through an error, both pipes are left

open. How long will it take to fill the pool?

Brain Busters Extend the concepts ofExample 3to solve each problem.

43.A cold-water faucet can fill a sink in 12 min, and a hot-water faucet can fill it in 15 min.

The drain can empty the sink in 25 min. If both faucets are on and the drain is open, how

long will it take to fill the sink?

44.Refer to Exercise 42.Assume that the error was discovered after both pipes had been run-

ning for 3 hr and the outlet pipe was then closed. How much more time would then be

required to fill the pool? (Hint:Consider how much of the job had been done when the

error was discovered.)

3

4

SECTION 7.8 Variation 475

Solve each equation for k. See Section 2.2.

Solve each formula for k. See Section 2.5.

49. 
    
    
    
    50. 
        
        
        
        51. 52.y=
        
        
        
        
    
    
    
    

k

x^2

y=

k

x

y=kx y=kx^2

92 =

k

2

180 =

k

20

200 = 15 k 25 = 9 k

PREVIEW EXERCISES

OBJECTIVES

Variation

7.8

1 Solve direct
variation problems.

2 Solve inverse
variation problems.

OBJECTIVE 1 Solve direct variation problems. Suppose that gasoline costs

$3.00 per gal. Then 1 gal costs $3.00, 2 gal costs 3 gal costs

and so on. Each time, the total cost is obtained by multiplying the

number of gallons by the price per gallon. In general, if kequals the price per gallon

and xequals the number of gallons, then the total cost yis given by y kx.

As the number of gallonsincreases,the total costincreases.

The following is also true.

As the number of gallons decreases,the total cost decreases.

The preceding discussion presents an example of variation.As in the gasoline

example, two variables vary directly if one is a constant multiple of the other.

=

31 $3.00 2 =$9.00,

21 $3.00 2 =$6.00,