AMC10 2010 B

AMC10 2010 B · Q10

AMC10 2010 B · Q10. 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?

谢尔比骑滑板车在不下雨时速度为 30 英里/小时，下雨时为 20 英里/小时。今天她早上在阳光下开车，晚上在雨中开车，总共 16 英里，用时 40 分钟。她在雨中开了多少分钟？

(A) 18 18

(B) 21 21

(D) 27 27

(E) 30 30

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $t$ be the number of minutes Shelby spent driving in the rain. Then she traveled $\frac{20t}{60}$ miles in the rain, and $\frac{30(40-t)}{60}$ miles in the sun. Solving $\frac{20t}{60}+\frac{30(40-t)}{60}=16$ results in $t=24$ minutes.

设 $t$ 为谢尔比在雨中开车的分钟数。那么她在雨中行驶了 $\frac{20t}{60}$ 英里，在阳光下行驶了 $\frac{30(40-t)}{60}$ 英里。解方程 $\frac{20t}{60}+\frac{30(40-t)}{60}=16$ 得到 $t=24$ 分钟。

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