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.She completes one lap in 100 seconds.What is her average speed?
A)2.5 m/s
B)5.0 m/s
C)10 m/s
D)0 m/s
E)1.3 m/s

Question

Quizplus · Accepted Answer

The total distance of the track is the sum of the lengths of the two parallel lines and the circumferences of the two semicircles. The length of the two parallel lines is $2 \times 96 = 192$ m. The circumference of a full circle with radius 49 m is $2\pi(49)$, so the total length of the two semicircles is $\pi(49)$. Therefore, the total distance is $192 + \pi(49) \times 2 = 192 + 98\pi$. The average speed is the total distance divided by the time, which is $\frac{192 + 98\pi}{100}$ m/s. This simplifies to approximately 5.0 m/s.

A Runner Runs Around a Track Consisting of Two Parallel