AMC8 2022

AMC8 2022 · Q22

AMC8 2022 · Q22. It mainly tests Rates (speed), Logic puzzles.

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?

一辆公交车从一站到下一站需要2分钟，并在每站停留1分钟让乘客上车。Zia步行从一站到下一站需要5分钟。当Zia到达一站时，如果公交车在前一站或已经离开前一站，她就等待公交车；否则她开始向下一站步行。假设公交车和Zia同时出发向图书馆前进，公交车落后3站。Zia何时上公交车？

(A) 17 17

(B) 19 19

(D) 21 21

(E) 23 23

Answer

Correct choice: (A)

正确答案：（A）

Solution

Initially, suppose that the bus is at Stop $0$ (starting point) and Zia is at Stop $3.$ We construct the following table of $5$-minute intervals: Note that Zia will wait for the bus after $15$ minutes, and the bus will arrive $2$ minutes later. Therefore, the answer is $15+2=\boxed{\textbf{(A) } 17}.$

初始时，假设公交车在第0站（起点），Zia在第3站。我们构建以下5分钟间隔的表格：注意Zia在15分钟后会等待公交车，公交车2分钟后到达。因此，答案是$15+2=\boxed{\textbf{(A) } 17}$。

Topics