1991 AHSME Problems/Problem 11

Jack and Jill run 10 km. They start at the same point, run 5 km up a hill, and reurn 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? The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.