Problem:
Three runners start running simultaneously from the same point on a -meter circular track. They each run clockwise around the course maintaining constant speeds of , and meters per second. The runners stop once they are all together again somewhere on the circular course. How many seconds do the runners run?
Answer Choices:
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B.
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E.
Solution:
Label the runners , and in increasing order of speed. After the start, runner and runner will be together again once runner has run an extra meters. Hence it takes seconds for runners and to be together again. Similarly, it takes seconds for runner and runner to be together again. Runners and will also be together at seconds, at which time all three runners will be together.
The problems on this page are the property of the MAA's American Mathematics Competitions