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?

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.