AMC12 2010 B

AMC12 2010 B · Q7

AMC12 2010 B · Q7. It mainly tests Linear equations, Rates (speed).

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?

Shelby骑她的滑板车在不下雨时以每小时$30$英里的速度行驶，下雨时以每小时$20$英里的速度行驶。今天她早上在晴天行驶，晚上在雨中行驶，总共在$40$分钟内行驶了$16$英里。她在雨中行驶了多少分钟？

(A) 18 18

(B) 21 21

(D) 27 27

(E) 30 30

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $x$ be the time it is not raining, and $y$ be the time it is raining, in hours. We have the system: $30x+20y=16$ and $x+y=\frac{2}{3}$ Solving gives $x=\frac{4}{15}$ and $y=\frac{2}{5}$ We want $y$ in minutes, $\frac{2}{5} \cdot 60=24 \Rightarrow C$

设不下雨时行驶时间为$x$小时，下雨时行驶时间为$y$小时。有方程组：$30x+20y=16$且$x+y=\frac{2}{3}$。解得$x=\frac{4}{15}$，$y=\frac{2}{5}$。将$y$换算成分钟：$\frac{2}{5}\cdot 60=24 \Rightarrow C$。

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