¶ 2022 AMC8 Problem 22
Problem:
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?
Answer Choices:
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Solution:
Refer to the figure below. The numbers above the line show the time in minutes when the bus arrives at and leaves each stop. The numbers below the line show the time in minutes when Zia reaches each stop.
When Zia arrives at bus stop after minutes, she notices that the bus is just leaving the previous stop, so she will wait for the bus. She will board the bus as soon as it arrives at , after minutes.
The bus and Zia begin stops apart, with the bus traveling stop in minutes and Zia traveling stop in minutes. She will wait for the bus when it is within stop from her, so the bus needs to make up a distance of stops. In the time Zia travels stop in minutes, the bus travels stops, reducing the distance between them by stop. It will take of Zia’s stops before the bus is close enough for her to wait. That will happen after minutes when she is at her third stop and the bus is leaving the previous stop. Zia will wait more minutes for the bus to arrive. She will board the bus after a total of minutes.
Answer: .
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