Question

Two runners are to race one lap on a circular track. The radius to the inside track. The radius to the inside lane is 50 meters. The radius to the outside lane is 51 meters. How much of a head start should the runner on the outside get?

Answer 1

If each guy stays in his own lane, then each one runs the
circumference of his circle.

Circumference of the lane with 50 meters radius = (2 x 50) π .

Circumference of the lane with 51 meters radius = (2 x 51) π .

The circumference of the outer lane is 2π meters greater than
the circumference of the inner lane. So the runner in the outside
lane should have a head start of 2π meters = 6.2832 meters

= 20 feet 7.4 inches.