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:: Escalator at the Tube ::

One morning, Ben is in a hurry to get off the station for work as he approaches the escalator at the tube station, but Fred is in an even bigger hurry. For every 2 steps Ben takes, Fred takes 3. Altogether Fred took 25 steps before getting off the escalator, while Ben took 20. Both of them step on every step.

How many steps does the escalator have showing at any given time?

Answer: 50

Let's assume the escalator moves at E steps/sec and there are n steps showing at any given time.

Fred took 25 steps on the escalator, which means his stepping rate is 25 divided by (n-25)/E, the total time he spent on the escalator, giving 25E/(n-25).

Similarly, Ben took 20 steps, which means his step rate is 20E/(n-20).

Since for every 2 steps Ben takes, Fred takes 3, this gives

3 x 20E/(n-20) = 2 x 25E/(n-25)

or n = 50.

Here the speed of the escalator E does not affect the solution.

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