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. 

It is close to 200 because 150 or above would be rounded to 200. Below 150 would be 100