1991 AHSME Problem 11

Jack and Jill run 10 km. They start at the same point, run 5 km up a hill, and return to the starting point by the same route. Jack has a 10 minute head start and runs at the rate of 15 km/hr uphill and 20 km/hr downhill. Jill runs 16 km/hr uphill and 22 km/hr downhill. How far from the top of the hill are they when they pass each other going in opposite directions (in km)?

\textbf{(A) } \frac{5}{4}\qquad \textbf{(B) } \frac{35}{27}\qquad \textbf{(C) } \frac{27}{20}\qquad \textbf{(D) } \frac{7}{3}\qquad \textbf{(E) } \frac{28}{49}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.