SOLUTION: A running track has straight parallel sides and semicircular ends. Each lane is one meter wide. How much head start should the runner in the outside lane receive over the runner in

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Question 252229: A running track has straight parallel sides and semicircular ends. Each lane is one meter wide. How much head start should the runner in the outside lane receive over the runner in the second lane from the outside so that they will each cover the same distance in one lap around the track?
A. 1 meter B. 2 meters C.pi meters D. 3/2 pi meters E. 2 pi meters
Answer by Theo(13342) About Me  (Show Source):
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since it doesn't matter how long the straight parallel sides are because they will both cover the same distance when running on the straight parallel sides, the only thing we need to consider is what happens at each end.

put those 2 ends together by removing the straight parallel sides and you have a circle.

the runners will be running exactly 1 meter apart is a basic assumption of this problem.

the circumference of a circle is 2*pi*r.

the runner on the inside lane will run a distance of 2 * pi * r

the runner on the outside lane will run a distance of 2 * pi * (r+1)

the runner on the outside lane will run 2 * pi * (r+1) - 2 * pi * r more distance than the runner on the inside lane.

the difference becomes 2 * pi * 1 which means the runner on the outside lane will run 2 * pi more meters than the runner on the inside lane.

that would be selection E (2 pi meters).

example:

assume the ends of the track form a circle that is 50 meters in radius.

the runner on the inside lane runs 2 * pi * 50 meters.

the runner on the outside lane runs 2 * pi * 51 meters.

subtract 2 * pi * 50 from 2 * pi * 51 and you get 2 * pi * 1 meters more.

that equals 2 * pi meters more.

the straightaway is irrelevant to the problem. it could be any distance.