¶ 2023 AMC8 Problem 15
Problem:
Visvam walks half a mile to get to school each day. His route consists of city blocks of equal length and he takes one minute to walk each block. Today, after walking blocks, Visvam discovers that he has to make a detour, walking blocks of equal length instead of block to reach the next corner. From the time he starts his detour, at what speed, in miles per hour, must Visvam walk in order to arrive at school at his usual time?
Answer Choices:
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E.
Solution:
Viswam normally walks mile in minutes, which equals of an hour, so his usual speed is miles per hour. When he starts his detour, he normally would have blocks to go. Because of the detour, he actually has blocks to go, so Viswam’s speed must be miles per hour to arrive at school at his usual time.
Viswam normally takes minutes to get to school. His detour starts when he is halfway to school, so from that time he has of an hour to get there. He must walk blocks, and because blocks is mile, blocks is of a mile.
Therefore, to arrive at school at his usual time, Viswam’s speed must be miles per hour.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions