This activity provides a real-life context for working with proportionality, speed, rates, and units of measurement. It is designed to be accessible to secondary maths students at Key Stage 3.

Detailed teachers' notes for this activity are available on our NRICH website.

Triathlon and Fitness

Stage: 3 Challenge Level: Challenge Level:2Challenge Level:2

If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...

The triathlon is a sport which consists of three consecutive races, a swim, a bike race and finally a long run.

Adam, Ben and Charles all want to qualify for the Olympic triathlon.


Here are their results from a trial race:



Swimming 1500m

Cycling 40km

Running 10km


















Which athlete do you think burned the most calories?

Adam, Ben and Charles weigh approximately 70kg each
It is estimated that athletes of this weight burn energy at the following rates:

  • Swimming at 4.5km/h burns 600 kcal per hour
  • Cycling at 30km/h burns 900 kcal per hour
  • Running at 15km/h burns 1100 kcal per hour

Assuming that the rate at which calories are burned is directly proportional to the athletes' speed, estimate how many calories each of the three athletes burned during his race.


Are you surprised?
How can you explain your results?

Do you think the modelling assumptions are valid?



Notes and Background

Though several versions of the triathlon exist, in the Olympic Games, the athletes swim for 1500 meters, then cycle for 40 km and finally run for a further 10 km. As you can imagine, the athletes who compete for the triathlon must have high endurance in order to be able to complete all three races.

Further information

If you're finding hard to get started, try looking at this hint.

Detailed teachers' notes for this activity are available on our NRICH website.