Difference between revisions of "2016 AMC 8 Problems/Problem 4"
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| − | + | == Problem == | |
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| + | When Cheenu was a boy, he could run <math>15</math> miles in <math>3</math> hours and <math>30</math> minutes. As an old man, he can now walk <math>10</math> miles in <math>4</math> hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy? | ||
<math>\textbf{(A) }6\qquad\textbf{(B) }10\qquad\textbf{(C) }15\qquad\textbf{(D) }18\qquad \textbf{(E) }30</math> | <math>\textbf{(A) }6\qquad\textbf{(B) }10\qquad\textbf{(C) }15\qquad\textbf{(D) }18\qquad \textbf{(E) }30</math> | ||
==Solution== | ==Solution== | ||
| − | {{solution}} | + | When Cheenu was a boy, he could run <math>15</math> miles in <math>3</math> hours and <math>30</math> minutes <math>= 3\times60 + 30</math> minutes <math>= 210</math> minutes, thus running <math>\frac{210}{15} = 14</math> minutes per mile. Now that he is an old man, he can walk <math>10</math> miles in <math>4</math> hours <math>= 4 \times 60</math> minutes <math>= 240</math> minutes, thus walking <math>\frac{240}{10} = 24</math> minutes per mile. Therefore, it takes him <math>\boxed{\textbf{(B)}\ 10}</math> minutes longer to walk a mile now compared to when he was a boy. |
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| + | ~CHECKMATE2021 | ||
| + | |||
| + | ==Video Solution== | ||
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| + | https://youtu.be/I9neY-xoG90?si=tDSd8my8W8Mb7Lqp | ||
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| + | A solution so simple a 12-year-old made it! | ||
| + | |||
| + | ~Elijahman~ | ||
| + | ==Video Solution (THINKING CREATIVELY!!!)== | ||
| + | https://youtu.be/r92zdVMTamI | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | ==Video Solution== | ||
| + | |||
| + | https://youtu.be/gKjWxvyNSjk | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2016|num-b=3|num-a=5}} | ||
| + | {{MAA Notice}} | ||
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| + | Another Solution | ||
| + | From the question, the old man can travel five miles in two hours, so we can set both speeds to 15 miles. We can see that Cheenu as an old man takes 2hrs 30mins for him to travel 15 miles, which is also 150 minutes. We can then divide this by fifteen, which gives us 10, so the answwer is B) 10 | ||
Latest revision as of 10:42, 20 June 2024
Contents
Problem
When Cheenu was a boy, he could run 
miles in 
hours and 
minutes. As an old man, he can now walk 
miles in 
hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?
Solution
When Cheenu was a boy, he could run miles in hours and minutes 
minutes 
minutes, thus running 
minutes per mile. Now that he is an old man, he can walk miles in hours 
minutes 
minutes, thus walking 
minutes per mile. Therefore, it takes him 
minutes longer to walk a mile now compared to when he was a boy.
~CHECKMATE2021
Video Solution
https://youtu.be/I9neY-xoG90?si=tDSd8my8W8Mb7Lqp
A solution so simple a 12-year-old made it!
~Elijahman~
Video Solution (THINKING CREATIVELY!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 2016 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
Another Solution From the question, the old man can travel five miles in two hours, so we can set both speeds to 15 miles. We can see that Cheenu as an old man takes 2hrs 30mins for him to travel 15 miles, which is also 150 minutes. We can then divide this by fifteen, which gives us 10, so the answwer is B) 10
