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Weekly Problem 40 - 2007

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Escalator

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps.

The taller of the two people climbs three times as quickly as the smaller person. He has counted the steps that he has taken in getting to the ticket barrier at the top; he took 75 steps.

The smaller person takes 50 steps on the escalator before getting to the top and the ticket barrier.

How many steps are there on the escalator that is used?