CAYLEY 2013 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 \displaystyle\frac xy?

Answer Choices
A. \displaystyle\frac98
B. \displaystyle\frac75
C. \displaystyle\frac{15}{16}
D. \displaystyle\frac{9}{16}
E. \displaystyle\frac{10}{9}