A man can walk up a moving "up" escalator in 30 seconds. He can walk down this moving "up" escalator in 1-1/2 minutes. If his walking pace is the same going upstairs as downstairs, how long would it take him to climb the escalator if it was stationary? How long would it take him to go up the moving escalator if he stood still?

VIEW SOLUTION BELOW

THE SOLUTION

Averaging the times for a result of 1 minute is incorrect in both cases. In 1 1/2 minutes the man can walk down 1 moving escalator or up 3. In 3 minutes walking, half the time up and half the time down, he can walk four escalator lengths. This is his walking pace - four escalator lengths in 3 minutes - for the effect of the moving escalator is cancelled. He can, therefore, climb or descend the still escalator in 1/4 of 3 minutes, that is, 45 seconds. In the 1 1/2 minutes required to walk down the moving up escalator, he walks the equivalent of two still escalators. Therefore the escalator must have moved up once in that time and its speed is one length in 1 1/2 minutes.