Question

Moe 用割草机修剪一块 $90$ 英尺乘 $150$ 英尺的长方形草坪。割草机每次割出的草带宽 $28$ 英寸，但他每次会重叠 $4$ 英寸，以确保没有漏割。他推割草机时的速度是每小时 $5000$ 英尺。下列哪一项最接近 Moe 修剪完草坪所需的小时数？

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?

$0.75$

$0.8$

$1.35$

$1.5$

$3$

答案：C

知识点：速率面积单位换算

难度评级：1270

小提示：

因为有重叠，每次实际新增割草宽度为 $28 - 4 = 24$ 英寸

Each pass effectively cuts a strip only $28 - 4 = 24$ inches wide because of the overlap

大提示：

$24$ 英寸就是 $2$ 英尺，所以每走一英尺就割 $2$ 平方英尺

A $24$ -inch strip is $2$ feet wide, so each foot walked mows $2$ square feet

解答：

因为重叠，每次新增的草带宽度为 $28 - 4 = 24$ 英寸 $= 2$ 英尺。所以 Moe 每走一英尺就割 $2$ 平方英尺，也就是每小时割 $2 \cdot 5000 = 10000$ 平方英尺。

草坪面积为 $90 \cdot 150 = 13500$ 平方英尺，所以所需时间为 $\frac{13500}{10000} = 1.35$ 小时。

因此，正确答案是 C。

Because of the overlap, each pass adds a strip $28 - 4 = 24$ inches $= 2$ feet wide. So each foot Moe walks mows $2$ square feet, that is, $2 \cdot 5000 = 10000$ square feet per hour.

The lawn has area $90 \cdot 150 = 13500$ square feet, so the time is $\frac{13500}{10000} = 1.35$ hours.

Thus, the correct answer is C.

2003 AMC 12B 第 4 题

答案：C

难度评级：1270

小提示：

大提示：

解答：

其他年份的第 4 题