AMC 12 2011b Problem 8

Keiko walks once around a track at exactly the same constant speed every day. The sides of the track are straight, and the ends are semicircles. The track has width $6$ meters, and it takes her $36$ seconds longer to walk around the outside edge of the track than around the inside edge. What is Keiko's speed in meters per second?

\textbf{(A)}\ \frac{\pi}{3} \textbf{(B)}\ \frac{2\pi}{3} \textbf{(C)}\ \pi \textbf{(D)}\ \frac{4\pi}{3} \textbf{(E)}\ \frac{5\pi}{3}