Alan and Bill are going to have a 400-meter race, but Alan gets a head start because he is slower. Their best times of the season are 82 seconds and 76 seconds

Question

Alan and Bill are going to have a 400-meter race, but Alan gets a head start because he is slower. Their best times of the season are 82 seconds and 76 seconds, respectively. How much (distance in meters) of a head start should Alan get? (Round your answer to the nearest whole number.)

Answer 1

Well suppose Alan gets an x metre head start.

Top speeds are 400/82 m/s for Alan, and 400/76 m/s for Bill.

Assuming they finish at the same time

Bill takes 76s to run the 400 m.

Alan runs (400-x) m, at a speed of 400/82 m/s, taking 76 s

So distance = speed x time, so (400-x) = 76 x 400/82 giving x = 29.3 m