Problem:
It takes Clea seconds to walk down an escalator when it is not operating, and only seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it?
Answer Choices:
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Solution:
Let be Clea's rate of walking and be the rate of the moving escalator. Because the distance is constant, . Solving for yields . Let be the time required for Clea to make the escalator trip while just standing on it. Then , so . Therefore seconds.
The problems on this page are the property of the MAA's American Mathematics Competitions