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2008 AMC 10A Problem 11

Problem 11 of 25IntermediateArithmetic

While Steve and LeRoy are fishing 11 mile from shore, their boat springs a leak, and water comes in at a constant rate of 1010 gallons per minute. The boat will sink if it takes in more than 3030 gallons of water. Steve starts rowing toward the shore at a constant rate of 44 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?

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Solution

At 44 miles per hour, Steve rows 11 mile in 1515 minutes. During that time 15⋅10=15015 \cdot 10 = 150 gallons enter. To stay under 3030 gallons, LeRoy must bail 150−30=120150 - 30 = 120 gallons in 1515 minutes, or 12015=8\dfrac{120}{15} = 8 gallons per minute. Thus, the correct answer is D.
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