52.During the first part of a trip on the highway, Jim and Annie averaged 60 mph. In Hous-
ton, traffic caused them to average only 30 mph. The distance they drove in Houston was
100 mi less than their distance on the highway. What was their total driving distance if
they spent 50 min more on the highway than they did in Houston?
Solve each problem. See Example 8.
Find k,given that and. See Section 2.1.
- 66.y=
k
x^2
y=
k
x
y=kx y=kx^2
y= 1 x= 3
PREVIEW EXERCISES
Fractional
Time Working Part of the
Rate Together Job Done
Butch x
Peggy^1 x
12
1
15
Fractional
Time Working Part of the
Rate Together Job Done
Lou x
Janet^1 x
5
1
8
406 CHAPTER 7 Rational Expressions and Functions
53.Butch and Peggy want to pick up the
mess that their grandson, Grant, has
made in his playroom. Butch can do it in
15 min working alone. Peggy, working
alone, can clean it in 12 min. How long
will it take them if they work together?
54.Lou can groom Randy Smith’s dogs in
8 hr, but it takes his business partner,
Janet, only 5 hr to groom the same dogs.
How long will it take them to groom
Randy’s dogs if they work together?
55.Jerry and Kuba are laying a hardwood floor. Working alone, Jerry can do the job in 20 hr.
If the two of them work together, they can complete the job in 12 hr. How long would it
take Kuba to lay the floor working alone?
56.Mrs. Disher is a high school mathematics teacher. She can grade a set of chapter tests in 5 hr
working alone. If her student teacher Mr. Howes helps her, it will take 3 hr to grade the
tests. How long would it take Mr. Howes to grade the tests if he worked alone?
57.Dixie can paint a room in 3 hr working alone. Trixie can paint the same room in 6 hr
working alone. How long after Dixie starts to paint the room will it be finished if Trixie
joins her 1 hr later?
58.Sheldon can wash a car in 30 min working alone. Leonard can do the same job in 45 min
working alone. How long after Sheldon starts to wash the car will it be finished if
Leonard joins him 5 min later?
59.If a vat of acid can be filled by an inlet pipe in 10 hr and emptied by an outlet pipe in 20 hr,
how long will it take to fill the vat if both pipes are open?
60.A winery has a vat to hold Zinfandel. An inlet pipe can fill the vat in 9 hr, while an outlet
pipe can empty it in 12 hr. How long will it take to fill the vat if both the outlet and the in-
let pipes are open?
61.Suppose that Hortense and Mort can clean
their entire house in 7 hr, while their toddler,
Mimi, can mess it up in only 2 hr. If Hortense
and Mort clean the house while Mimi is at her
grandma’s and then start cleaning up after
Mimi the minute she gets home, how long
does it take from the time Mimi gets home
until the whole place is a shambles?
62.An inlet pipe can fill an artificial lily pond in 60 min, while an outlet pipe can empty it in
80 min. Through an error, both pipes are left open. How long will it take for the pond to fill?