Boris, Spike and Percival are going to race up the 99 steps that lead from the beach to the car park at the top of the cliff. Boris can run up five steps in the same time as Spike can run up four steps, which is the same time as Percival can run up three steps. It is agreed that Boris starts from the bottom, Spike starts 21 steps up and Percival 38 steps up. If they all start at the same time, in
what order will they reach the top?
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.