2012 AMC 12B Problems/Problem 9

Problem

It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How seconds would it take Clea to ride the escalator down when she is not walking?

Solution

She walks at a rate of x units per second to travel a distance y. So 60x=y, and 24*(x+K)=y, where k is the speed of the escalator. so setting the two equations equal to each other, 60x=24x+24k, which means that 36x=24k; therefore, k=1.5x, so now divide 60 by 1.5 because you add the speed of the escalator but remove the walking, leaving the final answer that it takes 40 seconds to ride the escalator alone; answer choice B.