Question

Samia 骑自行车出发去拜访朋友，平均速度为每小时 $17$ 千米。当她骑完到朋友家一半的距离时，车胎漏气了，于是她以每小时 $5$ 千米的速度步行剩下的路程。她总共花了 $44$ 分钟到达朋友家。以千米为单位并四舍五入到小数点后一位，Samia 步行了多远？

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：1270

解答：

设总距离为 $2d$ ，因此她以 $17$ 千米/小时骑了 $d$ 千米，又以 $5$ 千米/小时走了 $d$ 千米。总时间（小时）满足左边合并得到 $\dfrac{22d}{85} = \dfrac{11}{15}$ ，所以 $d = \dfrac{11}{15} \cdot \dfrac{85}{22} = \dfrac{17}{6} = 2.833\ldots$ 。她步行了约 $2.8$ 千米。 $\frac{d}{17} + \frac{d}{5} = \frac{44}{60}.$

所以正确答案是 C。

Let $2d$ be the total distance, so she biked $d$ at $17$ km/h and walked $d$ at $5$ km/h. The total time in hours is $\frac{d}{17} + \frac{d}{5} = \frac{44}{60}.$ Combining the left side gives $\dfrac{22d}{85} = \dfrac{11}{15},$ so $d = \dfrac{11}{15} \cdot \dfrac{85}{22} = \dfrac{17}{6} = 2.833\ldots$ She walked about $2.8$ kilometers.

Thus, the correct answer is C.

2017 AMC 12B 第 4 题

答案：C

难度评级：1270

解答：

其他年份的第 4 题