AHSME 1991 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)? $\text{(A) } \frac{5}{4} \text{(B) } \frac{35}{27} \text{(C) } \frac{27}{20} \text{(D) } \frac{7}{3} \text{(E) } \frac{28}{49}$