2017 AMC 10 A
Complete problem set with solutions and individual problem pages
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? (2017 AMC 10A Problem, Question#9)
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The distance from town to town is uphill, and since Minnie rides uphill at a speed of , it will take her hours. Next, she will ride from town to town , a distance of all downhill. Since Minnie rides downhill at a speed of , it will take her half an hour. Finally, she rides from town back to town , a flat distance of . Minnie rides on a flat road at , so this will take her hour. Her entire trip takes her hours. Secondly, Penny will go from town to town , a flat distance of . Since Penny rides on a flat road at , it will take her of an hour. Next Penny will go from town to town , which is uphill for Penny. Since Penny rides at a speed of uphill, and town and are apart, it will take her hours. Finally, Penny goes from Town back to town , a distance of downhill. Since Penny rides downhill at , it will only take her of an hour. In total, it takes her hours, which simplifies to hours and minutes. Finally, Penny's Hour Minute trip was minutes less than Minnie's Hour Minute Trip.
