Difference between revisions of "2017 AMC 10A Problems/Problem 9"
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==Problem== | ==Problem== | ||
| − | Minnie rides on a flat road at 20 kilometers per hour (kph), downhill at 30 kph, and uphill at 5 kph. Penny rides on a flat road at 30 kph, downhill at 40 kph, and uphill at 10 kph. Minnie goes from town A to town B, a distance of 10 km all uphill, then from town B to town C, a distance of 10 km all uphill, then from town B to town C, a distance of 15 km all downhill, and then back to town A, a distance of 20 km on the flat. | + | Minnie rides on a flat road at 20 kilometers per hour (kph), downhill at 30 kph, and uphill at 5 kph. Penny rides on a flat road at 30 kph, downhill at 40 kph, and uphill at 10 kph. Minnie goes from town A to town B, a distance of 10 km all uphill, then from town B to town C, a distance of 10 km all uphill, then from town B to town C, a distance of 15 km all downhill, and then back to town A, a distance of 20 km on the flat. Penny goes the other way around using the same route. How many more minutes does it take Minnie to complete the 45-km ride than it takes Penny? |
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| + | ==Solution== | ||
| + | The distance from town A to town B is 10km uphill, and since Minnie rides uphill at a speed of 5 kph, it will take her 2 hour. Next, she will ride from town B to town C, a distance of 15 km all downhill. Since Minnie rides downhill at a speed of 30 kph, it will take her half(.5) of an hour. Finally, she rides from town c back to town a, a flat distance of 20 km. Minnie rides on a flat road at 20 kph, so this will take her 1 hour. Her entire trip takes her 3.5 hours. | ||
| + | Secondly, Penny will go from town A to town C, a flat distance of 20km. Since penny rides on a flat road at 30 kph, it will take her two thirds(2/3) of an hour. Next Penny will go from town C to town B, which is uphill for Penny. Since penny rides at a speed of 10kph uphill, and town C and B are 15 km apart, it will take her one and a half(1.5) hours. Finally, Penny goes from Town B back to town A, a distance of 10km downhill. Since Penny rides downhill at 40 kph, it will only take her a quarter of an hour. In total, it takes her 29/12 hours, which simplifies to 2 hours and 25 minutes. | ||
| + | Finally, Penny's 2 Hour 25 Minute trip was 65 minutes less than Minnie's 3 Hour 30 Minute Trip | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2017|ab=A|num-b=8|num-a=10}} | {{AMC10 box|year=2017|ab=A|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 16:56, 8 February 2017
Problem
Minnie rides on a flat road at 20 kilometers per hour (kph), downhill at 30 kph, and uphill at 5 kph. Penny rides on a flat road at 30 kph, downhill at 40 kph, and uphill at 10 kph. Minnie goes from town A to town B, a distance of 10 km all uphill, then from town B to town C, a distance of 10 km all uphill, then from town B to town C, a distance of 15 km all downhill, and then back to town A, a distance of 20 km on the flat. Penny goes the other way around using the same route. How many more minutes does it take Minnie to complete the 45-km ride than it takes Penny?
Solution
The distance from town A to town B is 10km uphill, and since Minnie rides uphill at a speed of 5 kph, it will take her 2 hour. Next, she will ride from town B to town C, a distance of 15 km all downhill. Since Minnie rides downhill at a speed of 30 kph, it will take her half(.5) of an hour. Finally, she rides from town c back to town a, a flat distance of 20 km. Minnie rides on a flat road at 20 kph, so this will take her 1 hour. Her entire trip takes her 3.5 hours. Secondly, Penny will go from town A to town C, a flat distance of 20km. Since penny rides on a flat road at 30 kph, it will take her two thirds(2/3) of an hour. Next Penny will go from town C to town B, which is uphill for Penny. Since penny rides at a speed of 10kph uphill, and town C and B are 15 km apart, it will take her one and a half(1.5) hours. Finally, Penny goes from Town B back to town A, a distance of 10km downhill. Since Penny rides downhill at 40 kph, it will only take her a quarter of an hour. In total, it takes her 29/12 hours, which simplifies to 2 hours and 25 minutes. Finally, Penny's 2 Hour 25 Minute trip was 65 minutes less than Minnie's 3 Hour 30 Minute Trip
See Also
| 2017 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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