2003 AMC 10B Problem 5

Moe uses a mower to cut his rectangular

90

-foot by

150

-foot lawn. The swath he cuts is

28

inches wide, but he overlaps each cut by

4

inches to make sure that no grass is missed. He walks at the rate of

5000

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

The lawn has area

90 \cdot 150 = 13{,}500

square feet. Each foot Moe walks mows an effective strip

2

feet wide, so he mows

2 \cdot 5000 = 10{,}000

square feet per hour. The time needed is

\dfrac{13{,}500}{10{,}000}=1.35

hours. Thus, the correct answer is C.