Question

Samia 骑自行车去拜访朋友，平均速度为每小时 $17$ 千米。当她走完到朋友家的路程的一半时，轮胎漏气了，于是她以每小时 $5$ 千米的速度走完剩下的一半路程。

她总共花了 $44$ 分钟到达朋友家。四舍五入到最接近的十分之一千米，Samia 走了多远？

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?

$2.0$

$2.2$

$2.8$

$3.4$

$4.4$

答案：C

知识点：路程、速度与时间一次方程

难度评级：1220

解答：

设她步行的距离为 $d$ 。因为这等于她骑车的距离，记为 $d=\dfrac{17}{6}=2.833\ldots$ ，所以。再设她步行的时间为小时。因此骑车时间为。现在用速度的定义可得这推出所以因而因为，有约为 $2.8$ 。 $\dfrac{d}{17}+\dfrac{d}{5}=\dfrac{44}{60}.$

所以正确答案是 C。

Let $d$ be the distance Samia walked. She bicycled the same distance, so her total travel time gives $\dfrac{d}{17}+\dfrac{d}{5}=\dfrac{44}{60}.$ Solving yields $d=\dfrac{17}{6}=2.833\ldots,$ which rounds to $2.8$ kilometers.

Thus, the correct answer is C .

2017 AMC 10B 第 7 题

答案：C

难度评级：1220

解答：

其他年份的第 7 题