Question

Keiko 每天以完全相同的恒定速度绕一条跑道走一圈。跑道两侧是直线，两端是半圆。跑道宽 $6$ 米，她绕外侧边缘走一圈比绕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 width $6$ 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：1330

小提示：

两条直线部分长度相同，所以内外边缘的差只来自弯曲的两端。

The straight portions have the same length on both edges, so only the curved ends differ

大提示：

两端的两个半圆合成整圆，且两个整圆半径相差 $6$ 。

The two semicircular ends form full circles whose radii differ by $6$

解答：

两条直线部分对两条路线相同，因此长度差只来自两个半圆端。设内侧半径为 $r$ ，则外侧多出的长度为 $2\pi(r+6)-2\pi r=12\pi\text{。}$

若速度为 $x$ 米每秒，则多用的时间给出 $36x=12\pi$ ，所以 $x=\dfrac{\pi}{3}$ 。

所以正确答案是 A。

The straight sides are the same length for both paths, so the difference in length comes only from the two semicircular ends. If the inner radius is $r,$ those ends combine into a full circle, and the extra length is $2\pi(r+6)-2\pi r=12\pi.$

If her speed is $x$ meters per second, then the extra time gives $36x=12\pi,$ so $x=\dfrac{\pi}{3}.$

Thus, the correct answer is A.

2011 AMC 12B 第 8 题

答案：A

难度评级：1330

小提示：

大提示：

解答：

其他年份的第 8 题