Relative velocity

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?

Harriet Hare and Turbo Tortoise want to cross the finish line together on their 12 mile race.... What time should Harriet set off?

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?

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