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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?

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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?

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Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?


Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Tom travels for $10$ minutes longer than Tim, a time of $1$ hour and $50$ minutes. 

Travelling at a speed of $60$ mph (or $1$ mile per minute), Tom travels a distance of $110$ miles.
Tim travelled the sam distance in $1$ hour $40$ minutes ($1\frac{2}{3}$ hours), so his speed, in mph was $110\div 1\frac{2}{3} = 110\times \frac{3}{5} = 22\times 3 = 66$ mph.

This problem is taken from the UKMT Mathematical Challenges.
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