AMC10 2017 B

AMC10 2017 B · Q7

AMC10 2017 B · Q7. It mainly tests Linear equations, 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 骑自行车以平均时速 17 公里的速度去朋友家。当她走了到朋友家一半的距离时，轮胎爆了，她步行剩余距离，时速 5 公里。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 d/17 + d/5 = 44/60 hours. Solving this equation yields d = 17/6 = 2.833…. Therefore Samia walked about 2.8 kilometers.

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

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