Question

Clea 在自动扶梯不运行时走下去需要 $60$ 秒；自动扶梯运行时，她走下去只需要 $24$ 秒。如果自动扶梯运行而她只是站着不动，她需要多少秒到达底部？

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?

$36$

$40$

$42$

$48$

$52$

答案：B

知识点：速率路程、速度与时间

难度评级：1280

解答：

设 $d$ 为扶梯的长度， $c$ 为 Clea 在静止扶梯上步行的速度， $e$ 为运行扶梯本身的速度。由速度等于路程除以时间， $c = \dfrac d{60}$ ，且因此这表明她站着不动时需要 $40$ 秒。 $c+e = \dfrac d{24}.$ $e = \dfrac d{24}-\dfrac d{60} = \dfrac d{40},$

所以正确答案是 B。

Let $d$ be the escalator's length, and let $c$ represent Clea's speed walking down the non-operational escalator. Similarly, let $e$ represent Clea's speed standing still on the operational escalator. Then, as speed is equal to distance over time, we know that $c = \dfrac d{60}$ and $c+e = \dfrac d{24}.$ Therefore, $e = \dfrac d{24}-\dfrac d{60} = \dfrac d{40},$ meaning that Clea takes $40$ seconds to descend the escalator by simply standing still.

Thus, the correct answer is B .

2012 AMC 10B 第 13 题

答案：B

难度评级：1280

解答：

其他年份的第 13 题