2022 AMC 8 第 22 题
先试着解答 2022 AMC 8 第 22 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2022 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
22.
公交车从一个站开到下一站需要 分钟，并在每站等 分钟让乘客上车。Zia 从一个公交站走到下一站需要 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 站。多少分钟后 Zia 会上公交车？
A bus takes minutes to drive from one stop to the next, and waits minute at each stop to let passengers board. Zia takes 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 stops behind. After how many minutes will Zia board the bus?
小提示：
只在 Zia 到达公交站时检查她的决定
Check Zia’s decision only when she reaches a stop
大提示：
比较 、、 分钟时两者的位置
Compare positions at , , and minutes
解答：
公交车需要 分钟开到下一站，再等 分钟，所以每 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 分钟一次。以公交车出发站为第零站，则 Zia 从第 站出发。
分钟后，Zia 在第 站，公交车在第 站等待，她继续走。 分钟后，Zia 在第 站，公交车在第 站和第 站之间，她继续走。 分钟后，Zia 在第 站，公交车在第 站，正好是前一站，所以她停下等待。
公交车再用 分钟到达她所在的站，所以她在 分钟后上车。
正确答案是 A。
The bus takes minutes to drive to the next stop and then waits minute, so it moves through one-stop cycles every minutes.
Zia makes a decision only when she reaches a stop, every minutes. Measure stops from the bus’s starting stop. Zia starts at stop .
After minutes, Zia is at stop , while the bus is waiting at stop , so she keeps walking. After minutes, Zia is at stop , while the bus is between stops and , so she keeps walking. After minutes, Zia is at stop , while the bus is at stop , the previous stop, so she waits.
The bus then takes more minutes to reach her stop, so she boards after minutes.
Thus, the correct answer is A.
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