Question

Andrea 和 Lauren 相距 $20$ 千米。她们骑自行车相向而行，其中 Andrea 的速度是 Lauren 的三倍，两人之间的距离以每分钟 $1$ 千米的速度缩短。 $5$ 分钟后，Andrea 因爆胎停止骑行并等待 Lauren。从她们开始骑车算起，Lauren 过多少分钟到达 Andrea 所在位置？

Andrea and Lauren are $20$ kilometers apart. They bike toward one another with Andrea traveling three times as fast as Lauren, and the distance between them decreasing at a rate of $1$ kilometer per minute. After $5$ minutes, Andrea stops biking because of a flat tire and waits for Lauren. After how many minutes from the time they started to bike does Lauren reach Andrea?

$20$

$30$

$55$

$65$

$80$

答案：D

知识点：路程、速度与时间速率

难度评级：1510

解答：

设 Lauren 的速度为 $r$ 千米/分钟。则 $r + 3r = 1$ ，所以 $r = \dfrac14$ 。

前 $5$ 分钟间距缩短 $5$ 千米，还剩 $15$ 千米。Lauren 独自以 $\dfrac14$ 千米/分钟走完，需 $\dfrac{15}{1/4} = 60$ 分钟。

总时间为 $5 + 60 = 65$ 分钟。

所以正确答案是 D。

Let Lauren's rate be $r$ km/min. Then $r + 3r = 1,$ so $r = \dfrac14.$

In the first $5$ minutes the gap shrinks by $5$ km, leaving $15$ km. Lauren covers this alone at $\dfrac14$ km/min, taking $\dfrac{15}{1/4} = 60$ minutes.

The total time is $5 + 60 = 65$ minutes.

Thus, the correct answer is D.

2009 AMC 10A 第 20 题

答案：D

难度评级：1510

解答：

其他年份的第 20 题