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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B.
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E.
Solution:
Since a bus stop takes minutes to drive and minute at every stop, the bus takes minutes at every stop. Zia can only stop at every minute interval, as that is when she arrives at a bus stop and chooses whether to stop or continue. Therefore, we can consider the time Zia stops by looking at each of their locations at these intervals. After minutes, Zia is stops from where the bus started. After minutes, Zia is stops from where the bus started. Meanwhile, the bus is stops from where it started, waiting. Zia therefore doesn't stop here. After minutes, Zia is stops from where the bus started. Meanwhile, the bus is between the rd and th stops from where it started. Zia therefore doesn't stop here. After minutes, Zia is stops from where the bus started. Meanwhile, the bus is stops from where it started, about to leave. Since the bus is at the previous stop, she will wait here. It will then take more minutes to get to Zia, so the total time was minutes.
Thus, the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions