Problem:
Minnie rides on a flat road at kilometers per hour (kph), downhill at , and uphill at . Penny rides on a flat road at , downhill at , and uphill at . Minnie goes from town to town , a distance of all uphill, then from town to town , a distance of all downhill, and then back to town , a distance of on the flat. Penny goes the other way around using the same route. How many more minutes does it take Minnie to complete the ride than it takes Penny?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that Penny is going downhill on the segment on which Minnie is going uphill, and vice versa. Minnie needs hours to go from to , hours to go from to , and hours to go from to , a total of hours. Penny's time is hours. It takes Minnie hours, which is minutes, longer.
The problems on this page are the property of the MAA's American Mathematics Competitions