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2012 AMC 10B Problems/Problem 13

Revision as of 17:41, 26 February 2012 by Jm314 (talk | contribs) (Created page with "== Solution == The same distance is being covered in each of the three scenarios. Let s be the speed of the escalator and c be the speed of Clea. Using d = v t, the first statem...")
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Solution

The same distance is being covered in each of the three scenarios. Let s be the speed of the escalator and c be the speed of Clea. Using d = v t, the first statement can be translated to the equation d = 60c. The second statement can be translated to d = 24(c+s). Equating and solving for s we find: s = 3c/2. The problem asks for the time it takes her to ride down the escalator. Since t = d/s and d = 60c, we have t = 60c/(3c/2) = 40.

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