AMC10 2012 B

AMC10 2012 B · Q13

AMC10 2012 B · Q13. It mainly tests Linear equations, Rates (speed).

It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it?

Clea走下静止的自动扶梯需要60秒，走下运行中的自动扶梯需要24秒。Clea只是站在运行中的自动扶梯上向下乘坐需要多少秒？

(A) 36 36

(B) 40 40

(D) 48 48

(E) 52 52

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Let $x$ be Clea's rate of walking and $r$ be the rate of the moving escalator. Because the distance is constant, $24(x+r)=60x$. Solving for $r$ yields $r=\frac{3}{2}x$. Let $t$ be the time required for Clea to make the escalator trip while just standing on it. Then $rt=60x$, so $\frac{3}{2}xt=60x$. Therefore $t=40$ seconds.

答案（B）：设 $x$ 为 Clea 的步行速度，$r$ 为自动扶梯的运行速度。由于路程恒定，有 $24(x+r)=60x$。解得 $r=\frac{3}{2}x$。设 $t$ 为 Clea 站在扶梯上不走动完成全程所需的时间，则 $rt=60x$，所以 $\frac{3}{2}xt=60x$。因此 $t=40$ 秒。

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