math
posted by Raheem on .
The track coach plans to make 8 lanes each 1meter wide on the running track. The track measures y meters along the inside curb. The track has straight parallel sides and semicircular ends. If the runners in a race lined up at the same spot and stayed in their own lanes throughout the race, they would not run the same distance. To make the race even, by how much should each lane be staggered?

Without knowing the radius of the semicircular ends, this can't be solved. However, given that the radius is r on the inside lane, the circular part of the lane has circumference 2πr. The straight part is the same length for each lane.
So, the radii for the lanes are
r, r+1, r+2 ... r+7
Thus each lane is 2π meters longer than the one inside it.