Difference between revisions of "2017 AMC 10A Problems/Problem 9"
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The distance from town <math>A</math> to town <math>B</math> is <math>10</math> km uphill, and since Minnie rides uphill at a speed of <math>5</math> kph, it will take her <math>2</math> hours. Next, she will ride from town <math>B</math> to town <math>C</math>, a distance of <math>15</math> km all downhill. Since Minnie rides downhill at a speed of <math>30</math> kph, it will take her half an hour. Finally, she rides from town <math>C</math> back to town <math>A</math>, a flat distance of <math>20</math> km. Minnie rides on a flat road at <math>20</math> kph, so this will take her <math>1</math> hour. Her entire trip takes her <math>3.5</math> hours. | The distance from town <math>A</math> to town <math>B</math> is <math>10</math> km uphill, and since Minnie rides uphill at a speed of <math>5</math> kph, it will take her <math>2</math> hours. Next, she will ride from town <math>B</math> to town <math>C</math>, a distance of <math>15</math> km all downhill. Since Minnie rides downhill at a speed of <math>30</math> kph, it will take her half an hour. Finally, she rides from town <math>C</math> back to town <math>A</math>, a flat distance of <math>20</math> km. Minnie rides on a flat road at <math>20</math> kph, so this will take her <math>1</math> hour. Her entire trip takes her <math>3.5</math> hours. | ||
Secondly, Penny will go from town <math>A</math> to town <math>C</math>, a flat distance of <math>20</math> km. Since Penny rides on a flat road at <math>30</math> kph, it will take her <math>\frac{2}{3}</math> of an hour. Next Penny will go from town <math>C</math> to town <math>B</math>, which is uphill for Penny. Since Penny rides at a speed of <math>10</math> kph uphill, and town <math>C</math> and <math>B</math> are <math>15</math> km apart, it will take her <math>1.5</math> hours. Finally, Penny goes from Town <math>B</math> back to town <math>A</math>, a distance of <math>10</math> km downhill. Since Penny rides downhill at <math>40</math> kph, it will only take her <math>\frac{1}{4}</math> of an hour. In total, it takes her <math>29/12</math> hours, which simplifies to <math>2</math> hours and <math>25</math> minutes. | Secondly, Penny will go from town <math>A</math> to town <math>C</math>, a flat distance of <math>20</math> km. Since Penny rides on a flat road at <math>30</math> kph, it will take her <math>\frac{2}{3}</math> of an hour. Next Penny will go from town <math>C</math> to town <math>B</math>, which is uphill for Penny. Since Penny rides at a speed of <math>10</math> kph uphill, and town <math>C</math> and <math>B</math> are <math>15</math> km apart, it will take her <math>1.5</math> hours. Finally, Penny goes from Town <math>B</math> back to town <math>A</math>, a distance of <math>10</math> km downhill. Since Penny rides downhill at <math>40</math> kph, it will only take her <math>\frac{1}{4}</math> of an hour. In total, it takes her <math>29/12</math> hours, which simplifies to <math>2</math> hours and <math>25</math> minutes. | ||
− | Finally, Penny's <math>2</math> Hour <math>25</math> Minute trip was <math>\boxed{\textbf{(C)}\ 65}</math> minutes less than Minnie's <math>3</math> Hour <math>30</math> Minute Trip. | + | Finally, Penny's <math>2</math> Hour <math>25</math> Minute trip was <math>\boxed{\textbf{(C)}\ 65}</math> minutes less than Minnie's <math>3</math> Hour <math>30</math> Minute Trip. |
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==Video Solution== | ==Video Solution== |
Revision as of 12:54, 20 August 2021
Contents
[hide]Problem
Minnie rides on a flat road at kilometers per hour (kph), downhill at kph, and uphill at kph. Penny rides on a flat road at kph, downhill at kph, and uphill at kph. Minnie goes from town to town , a distance of km all uphill, then from town to town , a distance of km all downhill, and then back to town , a distance of 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 -km ride than it takes Penny?
Solution
The distance from town to town is km uphill, and since Minnie rides uphill at a speed of kph, it will take her hours. Next, she will ride from town to town , a distance of km all downhill. Since Minnie rides downhill at a speed of kph, it will take her half an hour. Finally, she rides from town back to town , a flat distance of km. Minnie rides on a flat road at kph, so this will take her hour. Her entire trip takes her hours. Secondly, Penny will go from town to town , a flat distance of km. Since Penny rides on a flat road at kph, 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 kph uphill, and town and are km apart, it will take her hours. Finally, Penny goes from Town back to town , a distance of km downhill. Since Penny rides downhill at kph, 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.
Video Solution
~savannahsolver
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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