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2008 AMC 12A Problem 7

Problem 7 of 25EasierArithmetic

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

Rowing 11 mile at 44 miles per hour takes 14\tfrac{1}{4} hour, or 1515 minutes. In that time 15⋅10=15015 \cdot 10 = 150 gallons of water enter the boat. Since at most 3030 gallons may remain, LeRoy must bail 150−30=120150 - 30 = 120 gallons in 1515 minutes, a rate of 12015=8 \dfrac{120}{15} = 8 gallons per minute. Thus, D is the correct answer.
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