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In Constantly Passing

A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same direction. Buses leave the depot at regular intervals; they travel along the dual carriageway and back to the depot at a constant speed. At what interval do the buses leave the depot?

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Take a Message Soldier

A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?


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?