2019 Pascal Problem 23

A path of length 14 m consists of 7 unshaded stripes, each of length 1 m, alternating with 7 shaded stripes, each of length 1 m. A circular wheel of radius 2 m is divided into four quarters which are alternately shaded and unshaded. The wheel rolls at a constant speed along the path from the starting position shown.

The wheel makes exactly 1 complete revolution. The percentage of time during which a shaded section of the wheel is touching a shaded part of the path is closest to

\textbf{(A)}\ 20\%\quad \textbf{(B)}\ 18\%\quad \textbf{(C)}\ 16\%\quad \textbf{(D)}\ 24\%\quad \textbf{(E)}\ 22\%

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.