Problem:
Annie and Bonnie are running laps around a -meter oval track. They started together, but Annie has pulled ahead, because she runs faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?
Answer Choices:
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B.
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E.
Solution:
Let be the number of laps run by Annie when she passes Bonnie for the first time. The number of laps run by Bonnie is . Then . So .
For each lap Bonnie completes, Annie runs laps, thus gaining of a lap on Bonnie during that time. Annie will pass Bonnie when Bonnie has run laps, at which point Annie will have run .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions