### Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

### Illusion

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

### Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

# Bike Shop

##### Stage: 3 Short Challenge Level:

Suppose the distance to and from the bike shop is $x$ miles.
Then the time taken on the journey there is $\frac{x}{3}$ hours, and the time taken on the journey back is $\frac{x}{12}$ hours.

So altogether a distance of $2x$miles is travelled in $\frac{x}{3} + \frac{x}{12} = \frac{5x}{12}$ hours.

So the average speed is $2x \div \frac{5x}{12} = 4.8$ miles per hour.

This problem is taken from the UKMT Mathematical Challenges.