Question

Andy 的草坪面积是 Beth 草坪面积的两倍，也是 Carlos 草坪面积的三倍。Carlos 的割草机速度是 Beth 的一半，也是 Andy 的三分之一。若三人同时开始割各自的草坪，谁会最先完成？

Andy's lawn has twice as much area as Beth's lawn and three times as much area as Carlos' lawn. Carlos' lawn mower cuts half as fast as Beth's mower and one third as fast as Andy's mower. If they all start to mow their lawns at the same time, who will finish first?

Andy

Beth

Carlos

Andy 和 Carlos 并列第一。

Andy and Carlos tie for first.

三人同时完成。

All three tie.

答案：B

知识点：速率比与比例

难度评级：1370

解答：

设 Andy 的草坪面积为 $A$ ，则 Beth 的面积是 $\dfrac A2$ ，Carlos 的面积是 $\dfrac A3$ 。若 Carlos 的割草速度为 $R$ ，则 Beth 的速度为 $2R$ ，Andy 的速度为 $3R$ 。

三人的用时分别为 $\dfrac{A}{3R}$ 、 $\dfrac{A/2}{2R}=\dfrac{A}{4R}$ 、 $\dfrac{A/3}{R}=\dfrac{A}{3R}$ 。其中 $\dfrac{A}{4R}$ 最小。

所以 Beth 最先完成，正确答案是 B。

Let Andy's lawn have area $A;$ then Beth's is $\dfrac A2$ and Carlos' is $\dfrac A3.$ With Carlos' rate $R,$ Beth mows at $2R$ and Andy at $3R.$

Their times are $\dfrac{A}{3R},$ $\dfrac{A/2}{2R}=\dfrac{A}{4R},$ and $\dfrac{A/3}{R}=\dfrac{A}{3R}$ respectively. Beth's time $\dfrac{A}{4R}$ is the smallest, so Beth finishes first.

Thus, the correct answer is B.

2002 AMC 12B 第 17 题

答案：B

难度评级：1370

解答：

其他年份的第 17 题