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2012 AMC 12B Problem 9

Problem 9 of 25EasierAlgebra

It takes Clea 6060 seconds to walk down an escalator when it is not operating, and only 2424 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?

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Solution

Let xx be Clea’s walking rate and rr the escalator’s rate, with the length equal to 60x.60x. Walking on the moving escalator gives 24(x+r)=60x,24(x+r)=60x, so r=32x.r=\tfrac32x. Standing takes time tt with rt=60x,rt=60x, so 32xt=60x\tfrac32xt=60x and t=40t=40 seconds. Thus, the correct answer is B.

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Concepts: rate · system of equations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.