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?

$2$

$4$

$6$

$8$

$10$

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.

2008 AMC 12A Problem 7

Solution:

Problem 7 in Other Years