Difference between revisions of "2013 AMC 8 Problems/Problem 7"
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<math>\textbf{(A)}\ 60 \qquad \textbf{(B)}\ 80 \qquad \textbf{(C)}\ 100 \qquad \textbf{(D)}\ 120 \qquad \textbf{(E)}\ 140</math> | <math>\textbf{(A)}\ 60 \qquad \textbf{(B)}\ 80 \qquad \textbf{(C)}\ 100 \qquad \textbf{(D)}\ 120 \qquad \textbf{(E)}\ 140</math> | ||
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==Solution 1== | ==Solution 1== | ||
− | + | Clearly, for every <math>5</math> seconds, <math>3</math> cars pass. It's more convenient to have everything in seconds: <math>2</math> minutes and <math>45</math> seconds<math>=2\cdot60 + 45 = 165</math> seconds. We then set up a ratio: <cmath>\frac{3}{5}=\frac{x}{165}</cmath> | |
− | + | <cmath>3(165)=5x</cmath> | |
− | + | <cmath>x=3(33)=99\approx\boxed{\textbf{(C)}\ 100}.</cmath> | |
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+ | ~megaboy6679 ~MiracleMaths | ||
==Solution 2== | ==Solution 2== | ||
<math>2</math> minutes and <math>45</math> seconds is equal to <math>120+45=165\text{ seconds}</math>. | <math>2</math> minutes and <math>45</math> seconds is equal to <math>120+45=165\text{ seconds}</math>. | ||
− | Since | + | Since <math>6</math> cars pass at around <math>10</math> seconds, there are about <math>\left \lfloor{\dfrac{165}{10}}\right \rfloor =16</math> groups of <math>6</math> cars. There are about <math>16\cdot6=96\text{ cars}</math>, so the closest answer choice is <math>\boxed{\textbf{(C)}\ 100}</math>. |
− | ==Solution | + | ==Video Solution== |
− | + | https://www.youtube.com/watch?v=7avOfjhUT6Q | |
− | + | https://youtu.be/79lJItxCt50 ~savannahsolver | |
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==See Also== | ==See Also== | ||
{{AMC8 box|year=2013|num-b=6|num-a=8}} | {{AMC8 box|year=2013|num-b=6|num-a=8}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 00:20, 2 February 2023
Problem
Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?
Solution 1
Clearly, for every seconds, cars pass. It's more convenient to have everything in seconds: minutes and seconds seconds. We then set up a ratio:
~megaboy6679 ~MiracleMaths
Solution 2
minutes and seconds is equal to .
Since cars pass at around seconds, there are about groups of cars. There are about , so the closest answer choice is .
Video Solution
https://www.youtube.com/watch?v=7avOfjhUT6Q https://youtu.be/79lJItxCt50 ~savannahsolver
See Also
2013 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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.