Question

一段笔直的一英里高速公路关闭，路宽 $40$ 英尺。Robert 沿图示由半圆组成的路径骑自行车。如果他以每小时 $5$ 英里的速度骑行，走完这一英里路段需要多少小时？

注意：一英里等于五千二百八十英尺

A straight one-mile stretch of highway, $40$ feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at $5$ miles per hour, how many hours will it take to cover the one-mile stretch?

Note: 1 mile = 5280 feet

$\dfrac{\pi}{11}$

$\dfrac{\pi}{10}$

$\dfrac{\pi}{5}$

$\dfrac{2\pi}{5}$

$\dfrac{2\pi}{3}$

答案：B

知识点：弧单位换算路程、速度与时间

难度评级：1460

解答：

每个半圆让 Robert 沿公路前进 $40$ 英尺，所以一英里路段需要 $5280/40=132$ 个半圆。

每个半圆直径为 $40$ 英尺，因此弧长为 $20\pi$ 英尺。Robert 骑行总距离为 $132\cdot20\pi=2640\pi$ 英尺，也就是 $\dfrac{2640\pi}{5280}=\dfrac{\pi}{2}$ 英里。

速度为每小时 $5$ 英里，所以时间为 $\dfrac{\pi}{2}\div5=\dfrac{\pi}{10}$ 小时。

所以正确答案是 B。

Each semicircle advances Robert $40$ feet along the highway, so a one-mile stretch requires $5280/40=132$ semicircles.

Each semicircle has diameter $40$ feet, so its arc length is $20\pi$ feet. The total distance Robert rides is $132\cdot20\pi=2640\pi$ feet, which is $\dfrac{2640\pi}{5280}=\dfrac{\pi}{2}$ miles.

At $5$ miles per hour, the time is $\dfrac{\pi}{2}\div5=\dfrac{\pi}{10}$ hours.

Thus, B is the correct answer.

2014 AMC 8 第 25 题

答案：B

难度评级：1460

解答：

其他年份的第 25 题