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# Escalator

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Age 14 to 16

Challenge Level

- Problem
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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?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?