AMC12 2012 B

AMC12 2012 B · Q9

AMC12 2012 B · Q9. It mainly tests Linear equations, Rates (speed).

It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How many seconds would it take Clea to ride the escalator down when she is not walking?

当自动扶梯不运行时，Clea 走下去需要 60 秒；当自动扶梯运行时，她走下去需要 24 秒。如果 Clea 不走路，只是站在自动扶梯上乘下去，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

She walks at a rate of $x$ units per second to travel a distance $y$. As $vt=d$, we find $60x=y$ and $24*(x+k)=y$, where $k$ is the speed of the escalator. Setting the two equations equal to each other, $60x=24x+24k$, which means that $k=1.5x$. Now we divide $60$ by $1.5$ because you add the speed of the escalator but remove the walking, leaving the final answer that it takes to ride the escalator alone as $\boxed{\textbf{(B)}\ 40}$

她以每秒 $x$ 个单位的速度走过距离 $y$。由 $vt=d$，得 $60x=y$ 且 $24*(x+k)=y$，其中 $k$ 为自动扶梯的速度。令两式相等：$60x=24x+24k$，得到 $k=1.5x$。现在用 $60$ 除以 $1.5$，因为只保留自动扶梯速度而去掉行走速度，最终仅乘扶梯下行所需时间为 $\boxed{\textbf{(B)}\ 40}$。

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