Question

Sharon 通常以恒定速度从她家开车到她母亲家需要 $180$ 分钟。有一天，Sharon 以通常速度出发，但开了全程的 $\dfrac{1}{3}$ 后遇到严重暴风雪，于是把速度降低了每小时 $20$ 英里。这次行程总共用了 $276$ 分钟。从 Sharon 家到她母亲家有多少英里？

Driving at a constant speed, Sharon usually takes $180$ minutes to drive from her house to her mother's house. One day Sharon begins the drive at her usual speed, but after driving $\dfrac{1}{3}$ of the way, she hits a bad snowstorm and reduces her speed by $20$ miles per hour. This time the trip takes her a total of $276$ minutes. How many miles is the drive from Sharon's house to her mother's house?

$132$

$135$

$138$

$141$

$144$

答案：B

知识点：路程、速度与时间方程组

难度评级：1660

解答：

设距离为 $d$ 英里，通常速度为 $r$ mph。由于通常行程为 $3$ 小时， $d=3r$ 。

前 $\dfrac{1}{3}$ 路程以速度 $r$ 行驶，用时 $\dfrac{1}{3}\cdot180=60$ 分钟，所以剩下 $\dfrac{2}{3}$ 路程用时 $276-60=216$ 分钟， $=\dfrac{18}{5}$ 小时，速度为 $r-20$ 。

最后一段距离为 $\dfrac{2}{3}d=2r$ 英里，所以解得 $10r=18r-360$ ，因此 $r=45$ ， $d=3\cdot45=135$ 。 $2r=(r-20)\cdot\dfrac{18}{5}.$

所以正确答案是 B。

Let the distance be $d$ miles and the usual speed $r$ mph. Since the usual trip is $3$ hours, $d=3r.$

The first $\dfrac{1}{3}$ of the drive takes $\dfrac{1}{3}\cdot180=60$ minutes at speed $r,$ so the remaining $\dfrac{2}{3}$ takes $276-60=216$ minutes $=\dfrac{18}{5}$ hours at speed $r-20.$

That final portion covers $\dfrac{2}{3}d=2r$ miles, so $2r=(r-20)\cdot\dfrac{18}{5}.$ Solving gives $10r=18r-360,$ so $r=45$ and $d=3\cdot45=135.$

Thus, the correct answer is B.

2017 AMC 12A 第 13 题

答案：B

难度评级：1660

解答：

其他年份的第 13 题