AMC12 2003 B

AMC12 2003 B · Q4

AMC12 2003 B · Q4. It mainly tests Rates (speed), Rounding & estimation.

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 the lawn?

Moe 用割草机修剪他 $90$ 英尺乘 $150$ 英尺的矩形草坪。他每次割出的条带宽 $28$ 英寸，但为了确保不漏草，每次割草都会重叠 $4$ 英寸。他推着割草机行走的速度是每小时 $5000$ 英尺。以下哪个最接近 Moe 修剪完草坪所需的小时数？

(A) 0.75 0.75

(B) 0.8 0.8

(D) 1.5 1.5

(E) 3 3

Answer

Correct choice: (C)

正确答案：（C）

Solution

草坪面积为 $90\cdot150=13500$ 平方英尺。每次有效割草宽度为 $28-4=24$ 英寸，即 $2$ 英尺。Moe 每小时行走 $5000$ 英尺，因此每小时割草面积约为 $5000\cdot2=10000$ 平方英尺。所需时间约为 $\frac{13500}{10000}=1.35$ 小时。

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