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

小提示：

设她单程骑行的距离（也就是步行的距离）为 $d$ ；使用时间 $= \dfrac{\text{距离}}{\text{速度}}$ 。

Let $d$ be the one-way distance she biked (and also walked); use time $= \dfrac{\text{distance}}{\text{rate}}$

大提示：

解方程 $\dfrac{d}{17} + \dfrac{d}{5} = \dfrac{44}{60}$ ，求出 $d$ 。

Solve $\dfrac{d}{17} + \dfrac{d}{5} = \dfrac{44}{60}$ for $d$

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 $\frac{d}{17} + \frac{d}{5} = \frac{44}{60}\text{。}$ 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。

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

小提示：

大提示：

解答：

其他年份的第 4 题