1991 AHSME Problems/Problem 11
Problem
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)?
Solution
Consider the distance-time graph and use coordinate geometry, with time on the -axis and distance on the -axis. Thus Jack starts at and his initial motion, taking time in hours, is . This ends when , giving the point . He now runs in the opposite direction at km/hr, so the equation is . Now Jill starts at (as Jack has a head start of 10 minutes = hours), so her equation is Solving simultaneously with Jack's equation gives , so , and thus the required distance is
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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