Question

如果不下雨，Shelby 骑踏板车的速度为每小时 $30$ 英里；如果下雨，速度为每小时 $20$ 英里。今天上午她在晴天中骑行，傍晚在雨中骑行，共用 $40$ 分钟行驶了 $16$ 英里。她在雨中骑了多少分钟？

Shelby drives her scooter at a speed of $30$ miles per hour if it is not raining, and $20$ miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of $16$ miles in $40$ minutes. How many minutes did she drive in the rain?

$18$

$21$

$24$

$27$

$30$

答案：C

知识点：路程、速度与时间一次方程

难度评级：1370

解答：

$40$ 分钟是 $\frac{2}{3}$ 小时。设 Shelby 在晴天中骑了 $h$ 小时。

则雨中骑了 $\frac{2}{3} - h$ 小时，所以总路程为英里。这个值等于 $16$ ，因此 $30h + 20\left(\dfrac{2}{3} - h\right) = 10h + \dfrac{40}{3}$ $10h + \dfrac{40}{3} = 16$ $h = \dfrac{4}{15}.$

因此雨中骑行时间为 $60\left(\dfrac{2}{3} - \dfrac{4}{15}\right) = 60 \cdot \dfrac{2}{5} = 24$

所以正确答案是 C。

Note that $40$ minutes is $\frac{2}{3}$ hours. Let Shelby drive $h$ hours in the sun.

Then she drives $\frac{2}{3} - h$ hours in the rain, which means she travels a total of $30h + 20\left(\dfrac{2}{3} - h\right) = 10h + \dfrac{40}{3}$ miles. We have this equals $16,$ so $10h + \dfrac{40}{3} = 16$ $h = \dfrac{4}{15}.$

Then Shelby drives $60\left(\dfrac{2}{3} - \dfrac{4}{15}\right) = 60 \cdot \dfrac{2}{5} = 24$ minutes in the rain.

Thus, C is the correct answer.

2010 AMC 10B 第 10 题

答案：C

难度评级：1370

解答：

其他年份的第 10 题