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

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.

2008 AMC 10A Problem 11

Answer: D

Difficulty rating: 1280

Solution:

Problem 11 in Other Years