2022 AMC 8 Problem 22
Attempt Problem 22 of the 2022 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
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: A
Small hint:
Check Zia’s decision only when she reaches a stop
Big hint:
Compare positions at , , and minutes
Solution:
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.
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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- 1993 AMC 8
- 1994 AMC 8
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- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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