2008 AMC 12A Problem 7

Question

While Steve and LeRoy are fishing

1

mile from shore, their boat springs a leak, and water comes in at a constant rate of

10

gallons per minute. The boat will sink if it takes in more than

30

gallons of water. Steve starts rowing toward the shore at a constant rate of

4

miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?

2

4

6

8

10

Answer: D

Concepts:rate unit conversion

Difficulty rating: 1310

Small hint:

Find how many minutes the trip to shore takes

Big hint:

Water enters for

15

minutes, and at most

30

gallons may remain in the boat

Solution:

Rowing

1

mile at

4

miles per hour takes

\tfrac{1}{4}

hour, or

15

minutes. In that time

15 \cdot 10 = 150

gallons of water enter the boat.

Since at most

30

gallons may remain, LeRoy must bail

150 - 30 = 120

gallons in

15

minutes, a rate of

\dfrac{120}{15} = 8

gallons per minute.

Thus, D is the correct answer.