Difference between revisions of "2014 AMC 8 Problems/Problem 17"
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| + | ==Problem== | ||
George walks <math>1</math> mile to school. He leaves home at the same time each day, walks at a steady speed of <math>3</math> miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first <math>\frac{1}{2}</math> mile at a speed of only <math>2</math> miles per hour. At how many miles per hour must George run the last <math>\frac{1}{2}</math> mile in order to arrive just as school begins today? | George walks <math>1</math> mile to school. He leaves home at the same time each day, walks at a steady speed of <math>3</math> miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first <math>\frac{1}{2}</math> mile at a speed of only <math>2</math> miles per hour. At how many miles per hour must George run the last <math>\frac{1}{2}</math> mile in order to arrive just as school begins today? | ||
<math>\textbf{(A) }4\qquad\textbf{(B) }6\qquad\textbf{(C) }8\qquad\textbf{(D) }10\qquad \textbf{(E) }12</math> | <math>\textbf{(A) }4\qquad\textbf{(B) }6\qquad\textbf{(C) }8\qquad\textbf{(D) }10\qquad \textbf{(E) }12</math> | ||
| + | ==Solution 1== | ||
| + | Note that on a normal day, it takes him <math>1/3</math> hour to get to school. However, today it took <math>\frac{1/2 \text{ mile}}{2 \text{ mph}}=1/4</math> hour to walk the first <math>1/2</math> mile. That means that he has <math>1/3 -1/4 = 1/12</math> hours left to get to school, and <math>1/2</math> mile left to go. Therefore, his speed must be <math>\frac{1/2 \text{ mile}}{1/12 \text { hour}}=\boxed{6 \text{ mph}}</math>, so <math>\boxed{\text{(B) }6}</math> is the answer. | ||
| + | |||
| + | ==Video Solution (CREATIVE THINKING)== | ||
| + | https://youtu.be/Il6IcNHKkWk | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | |||
| + | |||
| + | == Video Solution == | ||
| + | https://youtu.be/rQUwNC0gqdg?t=3191 | ||
| + | |||
| + | ~ pi_is_3.14 | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/1jW0bwR_DPQ ~savannahsolver | ||
==See Also== | ==See Also== | ||
Latest revision as of 22:12, 7 May 2024
Contents
Problem
George walks 
mile to school. He leaves home at the same time each day, walks at a steady speed of 
miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first 
mile at a speed of only 
miles per hour. At how many miles per hour must George run the last mile in order to arrive just as school begins today?
Solution 1
Note that on a normal day, it takes him 
hour to get to school. However, today it took 
hour to walk the first 
mile. That means that he has 
hours left to get to school, and mile left to go. Therefore, his speed must be 
, so 
is the answer.
Video Solution (CREATIVE THINKING)
~Education, the Study of Everything
Video Solution
https://youtu.be/rQUwNC0gqdg?t=3191
~ pi_is_3.14
Video Solution
https://youtu.be/1jW0bwR_DPQ ~savannahsolver
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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. 
