Track Design

from nrich.maths.org/7359
 

Imagine you are building a new Olympic stadium and you are responsible for designing and marking out the running track. The track needs to fulfil the following specifications:
 


diagram of track


 
Can you work out the radius of the curved sections in order to produce an accurate scale drawing?

For the 200m race, runners start on the curved section at the right of the diagram and run anticlockwise to the finish line at the top left.
As the outer lanes are longer than the inner lanes, a staggered start is needed so that at the finish line all runners have run the same distance.
 
Can you work out where each runner should start so that they all run 200m in total?

For the 400m race, the runner in lane 1 does one complete lap of the track, so the start line is the same as the finish line. The runners in lanes 2 to 8 again have a staggered start.
 
Can you work out where each runner should start so that they all run 400m in total?