# Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line which is 100 km long.

The first train travels at a constant speed of 55 km/h. The second train travels at a constant speed of 70 km/h.

A very fast bee, Sidney travels at 100 km/h. Sidney 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?

Extension:

How could you alter the problem so that Sidney flies exactly 100
km?

*(Apologies to bee lovers everywhere!)*

The problem can be solved by considering the relative speed of the trains.

The speed of approach of the trains is 125 km/h on a 100 km track, so they will collide after a time 100/125 = 4/5 hour. Sidney flies at 100 km/h for 4/5 hour so he flies 80 km.

Finally, if Sidney were to fly exactly 100 km, the relative speed of the trains would be 100 km/h, provided Sidney was continuing to fly at 100 km/h. OR ..... there is another way - do you have any suggestions?

We received the correct solutions
from: **Stephen
Smith**(South Greenhoe Middle
School).