Question

Keiko 每天以完全相同的恒定速度绕跑道走一圈。跑道两侧为直线，两端为半圆。跑道宽 $6$ 米，她沿外侧边缘走一圈比沿内侧边缘走一圈多用 $36$ 秒。Keiko 的速度是多少米每秒？

Keiko walks once around a track at exactly the same constant speed every day. The sides of the track are straight, and the ends are semicircles. The track has a width of $6$ meters, and it takes her $36$ seconds longer to walk around the outside edge of the track than around the inside edge. What is Keiko's speed in meters per second?

$\dfrac{\pi}{3}$

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

$\pi$

$\dfrac{4\pi}{3}$

$\dfrac{5\pi}{3}$

答案：A

知识点：圆周长路程、速度与时间

难度评级：1370

解答：

设内侧半圆半径为 $r$ 。

内外路径的直线部分总长相同，所以距离差只来自两个半圆端。两个内侧半圆总长为 $2\pi r$ ，两个外侧半圆总长为 $2\pi(r+6)$ ，差为 $12\pi$ 。

Keiko 多用 $36$ 秒走了 $12\pi$ 米，所以速度为 $12\pi/36=\dfrac\pi3$ 米每秒。

所以正确答案是 A。

Let the inner semicircle radius be $r$ . The straight parts of the inside and outside paths have the same total length, so only the semicircular ends change the distance.

The two inner semicircles have total length $2\pi r$ , while the two outer semicircles have total length $2\pi(r+6)$ . The outside path is therefore $12\pi$ meters longer.

Keiko takes $36$ more seconds to walk $12\pi$ more meters, so her speed is $12\pi/36=\dfrac\pi3$ meters per second.

Thus, A is the correct answer.

2011 AMC 10B 第 12 题

答案：A

难度评级：1370

解答：

其他年份的第 12 题