How many steps on the escalator?

Question

An escalator moves steadily upwards. When you walk up it taking one step per second, you reach the top after stepping on 20 steps. When you walk up taking two steps per second, you reach the top after stepping on 32 steps.

How many steps are visible on the escalator when it is stopped? (That is, how many steps would you have to climb if it were switched off.)

Accepted Answer

80 steps. Set up. Let N be the number of steps on the stationary escalator, and let it move at e steps per second. - Trip 1: you take 1 step per second and step on 20 steps, so the trip lasts 20 seconds. In that time the escalator carries you 20e steps. Total: N = 20 + 20e. - Trip 2: you take 2 steps per second and step on 32 steps, so the trip lasts 16 seconds. The escalator carries you 16e steps. Total: N = 32 + 16e. Solve. 20 + 20e = 32 + 16e, so 4e = 12 and e = 3 steps per second. Then N = 20 + 60 = 80. Check. At two steps per second for 16 seconds you climb 32 steps while the escalator a…

How many steps on the escalator?

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