AMC12 2017 B

AMC12 2017 B · Q4

AMC12 2017 B · Q4. It mainly tests Rates (speed).

Samia set off on her bicycle to visit her friend, traveling at an average speed of 17 kilometers per hour. When she had gone half the distance to her friend's house, a tire went flat, and she walked the rest of the way at 5 kilometers per hour. In all it took her 44 minutes to reach her friend's house. In kilometers rounded to the nearest tenth, how far did Samia walk?

Samia 骑自行车去朋友家，平均速度为 17 公里/小时。当她走了一半距离时，轮胎爆了，她以 5 公里/小时的速度步行剩余路程。总共用了 44 分钟到达朋友家。四舍五入到十分位，Samia 步行了多少公里？

(A) 2.0 2.0

(B) 2.2 2.2

(D) 3.4 3.4

(E) 4.4 4.4

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $2d$ be the distance in kilometers to the friend’s house. Then Samia bicycled distance $d$ at rate 17 and walked distance $d$ at rate 5, for a total time of $\frac{d}{17} + \frac{d}{5} = \frac{44}{60}$ hours. Solving this equation yields $d = \frac{17}{6} \approx 2.833\dots$. Therefore Samia walked about 2.8 kilometers.

设到朋友家的距离为 $2d$ 公里。那么 Samia 骑车 $d$ 公里速率为 17，步行 $d$ 公里速率为 5，总时间 $\frac{d}{17} + \frac{d}{5} = \frac{44}{60}$ 小时。解此方程得 $d = \frac{17}{6} \approx 2.833\dots$。因此 Samia 步行了约 2.8 公里。

Topics

AR.007 Rates (speed)