Question

Lopez 先生上班有两条路线可选。路线 A 长 $6$ 英里，他在这条路线上的平均速度为每小时 $30$ 英里。路线 B 长 $5$ 英里，他在这条路线上的平均速度为每小时 $40$ 英里，但其中有一段 $\dfrac{1}{2}$ 英里的学校区域，平均速度为每小时 $20$ 英里。路线 B 比路线 A 快多少分钟？

Mr. Lopez has a choice of two routes to get to work. Route A is $6$ miles long, and his average speed along this route is $30$ miles per hour. Route B is $5$ miles long, and his average speed along this route is $40$ miles per hour, except for a $\dfrac{1}{2}$ -mile stretch in a school zone where his average speed is $20$ miles per hour. By how many minutes is Route B quicker than Route A?

$2 \dfrac{3}{4}$

$3 \dfrac{3}{4}$

$4 \dfrac{1}{2}$

$5 \dfrac{1}{2}$

$6 \dfrac{3}{4}$

答案：B

知识点：路程、速度与时间单位换算

难度评级：900

解答：

路线 A 所需时间为分钟。 $\dfrac{6}{30} \cdot 60 = 12$

路线 B 所需时间为分钟。 $\left(\dfrac{5 - .5}{40} + \dfrac{.5}{20}\right) \cdot 60 = 8.25$

因此路线 B 快 $12 - 8.25 = 3.75$ 分钟。

所以正确答案是 B。

Mr. Lopez would take $\dfrac{6}{30} \cdot 60 = 12$ minutes to travel on Route A.

On Route B, he would take $\left(\dfrac{5 - .5}{40} + \dfrac{.5}{20}\right) \cdot 60 = 8.25$ minutes.

The difference in times along these routes is $12 - 8.25 = 3.75$ minutes.

Thus, B is the correct answer.

2021 AMC 10A Fall 第 4 题

答案：B

难度评级：900

解答：

其他年份的第 4 题