An Unhappy End

Show the 'film' asking pupils to focus on the fly. Ask them what data they would need to analyse the situation mathematically, and provide the speeds and distance.

Ask students to begin calcuating times, distances and positions of the trains and the fly. They will need to establish a clear way of recording their results. Encourage them to describe their strategy, even if they are frustrated by the length of the task.

It is useful to discuss with students that in some circumstances, the only option for solving a problem is to find a long, complex algorithm. However, the frustration CAN be a trigger to step back and find more efficient methods, and in this case there is a good method.

The simple way of looking at this problem is the total time until collision of the two trains and the complicated way is working out the points at which the fly hits a train on each part of the journey and then adding these up. Ideally someone in the group will come up with the simpler method - if not, you could leave it as an open problem, or begin to encourage the group to focus on time.

Alter the distance between the engines or the speeds to change the problem.

If the fly flew for 1 minute, what could the distance and speeds have been?

If the fly flew 2000 metres, what could the distance and speeds have been?

Speedy Sidney provides a similar context for a slightly more challenging problem.

This problem is a perfect opportunity to think about infinite series - the fly makes infinitely many trips between the two trains before collision. The total time taken for all of the trips must equal the time taken for the trains to collide. Students might wish to investigate the creation of this series by working out how long the fly takes to travel on each portion of its journey.