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2003 AMC 12B Problem 4

Problem 4 of 25EasierGeometryArithmetic

Moe uses a mower to cut his rectangular 9090-foot by 150150-foot lawn. The swath he cuts is 2828 inches wide, but he overlaps each cut by 44 inches to make sure that no grass is missed. He walks at the rate of 50005000 feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawn?

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Solution

Because of the overlap, each pass adds a strip 28−4=2428 - 4 = 24 inches =2= 2 feet wide. So each foot Moe walks mows 22 square feet, that is, 2⋅5000=100002 \cdot 5000 = 10000 square feet per hour. The lawn has area 90⋅150=1350090 \cdot 150 = 13500 square feet, so the time is 1350010000=1.35 \frac{13500}{10000} = 1.35 hours. Thus, the correct answer is C.
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