2011 AMC 12B 第 8 题

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：

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