Solution to:
Escalator Exercise
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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