Question

公交车从一个站开到下一站需要 $2$ 分钟，并在每站等 $1$ 分钟让乘客上车。Zia 从一个公交站走到下一站需要 $5$ 分钟。当 Zia 到达一个公交站时，如果公交车在前一站，或已经离开前一站，那么她会等公交车。否则她会继续走向下一站。假设公交车和 Zia 同时朝图书馆方向出发，公交车在 Zia 后面 $3$ 站。多少分钟后 Zia 会上公交车？

A bus takes $2$ minutes to drive from one stop to the next, and waits $1$ minute at each stop to let passengers board. Zia takes $5$ minutes to walk from one bus stop to the next. As Zia reaches a bus stop, if the bus is at the previous stop or has already left the previous stop, then she will wait for the bus. Otherwise she will start walking toward the next stop. Suppose the bus and Zia start at the same time toward the library, with the bus $3$ stops behind. After how many minutes will Zia board the bus?

$17$

$19$

$20$

$21$

$23$

答案：A

知识点：过程模拟路程、速度与时间

难度评级：1510

解答：

公交车需要 $2$ 分钟开到下一站，再等 $1$ 分钟，所以每 $3$ 分钟完成一个站距周期。

Zia 只在到达公交站时做决定，也就是每 $5$ 分钟一次。以公交车出发站为第零站，则 Zia 从第 $3$ 站出发。

$5$ 分钟后，Zia 在第 $4$ 站，公交车在第 $2$ 站等待，她继续走。 $10$ 分钟后，Zia 在第 $5$ 站，公交车在第 $3$ 站和第 $4$ 站之间，她继续走。 $15$ 分钟后，Zia 在第 $6$ 站，公交车在第 $5$ 站。

公交车再用 $2$ 分钟到达她所在的站，所以她在 $17$ 分钟后上车。

正确答案是 A。

The bus takes $2$ minutes to drive to the next stop and then waits $1$ minute, so it moves through one-stop cycles every $3$ minutes.

Zia makes a decision only when she reaches a stop, every $5$ minutes. Measure stops from the bus's starting stop. Zia starts at stop $3$ .

After $5$ minutes, Zia is at stop $4$ , while the bus is waiting at stop $2$ , so she keeps walking. After $10$ minutes, Zia is at stop $5$ , while the bus is between stops $3$ and $4$ , so she keeps walking. After $15$ minutes, Zia is at stop $6$ , while the bus is at stop $5$ , the previous stop, so she waits.

The bus then takes $2$ more minutes to reach her stop, so she boards after $17$ minutes.

Thus, the correct answer is A.

2022 AMC 8 第 22 题

答案：A

难度评级：1510

解答：

其他年份的第 22 题