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

An Unhappy End

Age 11 to 14
Challenge Level

We had many correct solutions to this one including a spreadsheet from Brian, Michael, Jon, James, Eli and Sam from Queen's College Junior School in Taunton, showing how far the trains and fly had travelled at each second after the trains set off.

Thomas from Darley Dale Primary School explained his solution like this:

First, you had to work out the distance travelled before the two trains collided, thus causing the 'Unhappy Ending'. This worked out as 500m (half of 1000m.).
The time it took the trains to travel this distance at 10m per second was 50 seconds.
Therefore, the fly had 50 seconds before the trains collided.
As the fly flew at 25m per second, it travelled 1250m (50 times 25) before it met its 'unhappy ending.'

Joe from Haslingfield worked it out as follows:

The trains are 1000m apart.
They travel at the same speed which means they both cover 500m before they crash.
The fly travels at 2.5 times the speed of the trains so it covers 2.5 times the distance the trains do. Therefore the calculation you need to work out is 500m x 2.5 which equals 1250m.

Well done to you all and to everyone else who answered this problem correctly: Steven from Whybridge Junior School, Robert from Ardingly College Junior School, Charlotte from Winterton Juniors, Helena, Sarah and Tom from Colyton Grammar School, Samuel from Geneva English School, Charlie and Ian from William Lovell School, Natalie, Matilda and Laura, Elle and Cat from The Mount School, Mandy Appleyard from Ashlyns School, Lawrence from Beecroft Public School (NSW, Ausralia), Salma from Balwearie High School, Andrew and Yuming from The Perse School for Boys, Alex from St Edwards School, Matthew from Waverley Christian College, Sean from St. Andrew's School...