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Stonehenge

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Escalator

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. ... How many steps are there on the escalator?

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?

Take a Message Soldier

Age 14 to 18 Challenge Level:

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During an exercise a column of soldiers were marching at a constant speed. At the end of the column was a messenger. He was commanded to proceed to the head of the column, deliver a dispatch and return to his former position at the back of the column, without delay.

On regaining his former position he noticed that the end of the column was in the same position that the head of the column had occupied when he first left his own position.

What is the ratio of the messenger's speed to that of the column whilst this order was being carried out? (Assume that no time was wasted in delivering the message or returning to his former position.)