2012 AMC 10B Problems/Problem 13

Solution

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). Since the same distance is being covered in each scenario, we can set the two equations equal and solve for s to 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.