Question

Andy 的草坪面积是 Beth 的两倍，也是 Carlos 的三倍。Carlos 的割草机速度是 Beth 的一半，也是 Andy 的三分之一。如果他们同时开始修剪各自的草坪，谁最先完成？

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 的面积为 $\dfrac{A}{2}$ ，Carlos 的面积为 $\dfrac{A}{3}$ 。再设 Carlos 的速度为 $R$ ，Beth 和 Andy 的速度分别为 $2R$ 、 $3R$ 。

三人所需时间分别为 $\begin{aligned} &\text{Andy: } \dfrac{A}{3R}, \\ &\text{Beth: } \dfrac{A/2}{2R} = \dfrac{A}{4R}, \\ &\text{Carlos: } \dfrac{A/3}{R} = \dfrac{A}{3R}. \end{aligned}$

其中最短的是 $\dfrac{A}{4R}$ ，所以 Beth 最先完成。

所以正确答案是 B。

Let Andy's lawn have area $A,$ so Beth's is $\dfrac{A}{2}$ and Carlos' is $\dfrac{A}{3}.$ Let Carlos mow at rate $R,$ so Beth mows at $2R$ and Andy at $3R.$

The times are $\begin{aligned} &\text{Andy: } \dfrac{A}{3R}, \\ &\text{Beth: } \dfrac{A/2}{2R} = \dfrac{A}{4R}, \\ &\text{Carlos: } \dfrac{A/3}{R} = \dfrac{A}{3R}. \end{aligned}$

Since $\dfrac{A}{4R}$ is the smallest, Beth finishes first.

Thus, the correct answer is B.

2002 AMC 10B 第 21 题

答案：B

难度评级：1370

解答：

其他年份的第 21 题