2013 Cayley Problem 20

Jack and Jill exercise along the same route. Jill jogs the first half of the route at 6 km/h, runs the remainder of the route at 12 km/h and takes a total time of x hours. Jack walks the first third of the route at 5 km/h, runs the remainder at 15 km/h and takes a total time of y hours. Which of the following is equal to \dfrac{x}{y}?

\textbf{(A)}\ \frac{9}{8}\quad \textbf{(B)}\ \frac{7}{5}\quad \textbf{(C)}\ \frac{15}{16}\quad \textbf{(D)}\ \frac{9}{16}\quad \textbf{(E)}\ \frac{10}{9}

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 Cayley contests here.