2008 AMC 10A Problem 11

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: 1280

Small hint:

Find how many minutes Steve needs to row one mile

Big hint:

In that time

150

gallons enter, but the boat can hold only

30

Solution:

At

4

miles per hour, Steve rows

1

mile in

15

minutes. During that time

15 \cdot 10 = 150

gallons enter.

To stay under

30

gallons, LeRoy must bail

150 - 30 = 120

gallons in

15

minutes, or

\dfrac{120}{15} = 8

gallons per minute.

Thus, the correct answer is D.