A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m. He completes one lap in 2.0 minutes. What is his average speed?
A) 1.6 m/s
B) 4.2 m/s
C) 2.9 m/s
D) 0 m/s
E) 2.1 m/s

Question

Quizplus · Accepted Answer

The runner's average speed is the total distance he runs divided by the time it takes him to run that distance. The total distance is the length of the two parallel lines plus the circumference of the two semicircles. The length of the two parallel lines is 96 m, and the circumference of a semicircle is πr, where r is the radius of the semicircle. The radius of the semicircles is 49 m, so the circumference of each semicircle is π(49 m) = 153.94 m. The total distance is therefore 96 m + 153.94 m + 153.94 m = 403.88 m. The runner completes one lap in 2.0 minutes, which is 120 seconds. Therefore, his average speed is 403.88 m / 120 s = 3.366 m/s.

A Runner Runs Around a Track Consisting of Two Parallel