You walk upwards on an escalator, with a speed of 1 step per second. After 50 steps, you are at the end. You turn around and run downwards with a speed of 5 steps per second. After 125 steps, you are back at the beginning of the escalator.
How many steps do you need if the escalator stands still?

100 steps.

Let v be the speed of the escalator, in steps per second. Let L be the number of steps that you need to take when the escalator stands still.

Upwards (along with the escalator), you walk 1 step per second. You need 50 steps, so that takes 50 seconds. This gives the following equation:

L steps - 50 seconds × v steps/second = 50 steps.
Downwards (against the direction of the escalator), you walk 5 steps per second. You need 125 steps, so that takes 25 seconds. This gives the following equation:

L steps + 25 seconds × v steps/second = 125 steps.
From the two equations follows: L = 100, v = 1. When the escalator stands still, you need 100 steps.


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