Olympic Mathematics - Marathon problem-solving for Year 6

Story:

Your heart pumps through your chest. Sweaty palms. Uneven breathing. The starting gun fires! You are competing in the 100m sprint - go, go, go! Actually, wait a second, this is not the 100m sprint, it is the marathon (42.2km). If you keep up your sprint pace, will you beat the real Olympic athletes at their marathon pace? Let's see...

Tools: Stopwatches or tablets with stopwatch functionality.

Main event

• First, work out your sprint time for a 100m sprint.

• Considering the time it takes you to run 100 metres. If you could keep up that pace for an entire marathon (for running 42.2km or swimming 10km), how long would it take?

• Compare this to the actual Olympic/world records for marathons – how significant is the difference? What pace do marathon athletes run/swim at per 100m, and per kilometre? Can you run faster than a marathon athlete, even for just 100m?
  

Olympic records for comparison of your time: https://worldathletics.org/records/by-category/world-records

1. Can you beat a world record marathon pace over just 100m? That is, if you multiply your 100m to make it 42.2km (part of the challenge is to work out what to multiply by), then what is your 'sprinting marathon' time?

2. What is your pace per kilometre?

3. Next, compare your own 200m pace (run and time yourself again, but for double the distance). What would be your marathon time? What about for 400m?
   

4. Repeat for other distances: Compare the time it takes a world record athlete to run 1500m (pace per kilometre) and the pace of a marathon world record by kilometre. What is the difference in average pace per kilometre?

5. Repeat for the 5k race world record times, 10k race times, and other events that span for different distances (canoe sprint v. rowing the full length of the world's longest rivers; or sport climbing versus climbing the world's tallest mountains). How much faster is the shorter distance athlete, compared to the long distance athlete, if both were competing for the longer event's distance?

Support: Try the swimming marathon (10km). Compare the world record time for a 10km swim to your 100m sprint pace if it were for 10km. Who would win and by how much time? What about your 200m pace? Extreme support: Work out your pace per 1km, based on your 100m sprint. Then do a 200m sprint and work out your pace per kilometre. Then a 250m sprint. Then a 500m sprint. Finally, run an actual kilometre. Why was the pace different to what you had thought based on all the previous calculations?