AMC10 2011 B

AMC10 2011 B · Q12

AMC10 2011 B · Q12. It mainly tests Rates (speed), Area & perimeter.

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?

Keiko 每天以完全相同的恒定速度绕跑道走一圈。跑道两侧是直线，两端是半圆。跑道宽度 6 米，她绕外侧边缘走一圈比内侧边缘多花 36 秒。Keiko 的速度是多少米/秒？

(A) $\frac{\pi}{3}$ $\frac{\pi}{3}$

(B) $\frac{2\pi}{3}$ $\frac{2\pi}{3}$

(D) $\frac{4\pi}{3}$ $\frac{4\pi}{3}$

(E) $\frac{5\pi}{3}$ $\frac{5\pi}{3}$

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The only parts of the track that are longer walking on the outside edge rather than the inside edge are the two semicircular portions. If the radius of the inner semicircle is $r$, then the difference in the lengths of the two paths is $2\pi(r+6)-2\pi r=12\pi$. Let $x$ be her speed in meters per second. Then $36x=12\pi$, and $x=\frac{\pi}{3}$.

答案（A）：跑道上只有两段半圆部分，外侧边缘比内侧边缘更长。若内侧半圆的半径为$r$，则两条路径长度之差为$2\pi(r+6)-2\pi r=12\pi$。设$x$为她的速度（米/秒），则$36x=12\pi$，从而$x=\frac{\pi}{3}$。

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