## 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:

Lsteps - 50 seconds ×vsteps/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:

Lsteps + 25 seconds ×vsteps/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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