Difference between revisions of "1951 AHSME Problems/Problem 38"
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==Problem== | ==Problem== | ||
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| + | A rise of <math>600</math> feet is required to get a railroad line over a mountain. The grade can be kept down by lengthening the track and curving it around the mountain peak. The additional length of track required to reduce the grade from <math>3\%</math> to <math>2\%</math> is approximately: | ||
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| + | <math> \textbf{(A)}\ 10000\text{ ft.}\qquad\textbf{(B)}\ 20000\text{ ft.}\qquad\textbf{(C)}\ 30000\text{ ft.}\qquad\textbf{(D)}\ 12000\text{ ft.}\qquad\textbf{(E)}\ \text{none of these} </math> | ||
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==Solution== | ==Solution== | ||
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| + | A grade is the rise divided by the horizontal length for a given segment of track. This means we can get the horizontal length of the track by dividing the rise by the grade. | ||
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| + | At a <math>3\%</math> grade, the horizontal track length is <math>20000</math> feet. At a <math>2\%</math> grade, the horizontal track length is <math>30000</math> feet. The difference is <math>10000</math> feet of horizontal track. Compared to <math>10000</math>, <math>600</math> feet is insignificant and can be safely covered by the problem's use of the word "approximately." Therefore, the answer is <math>\boxed{\textbf{(A)}}</math>. | ||
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== See Also == | == See Also == | ||
{{AHSME 50p box|year=1951|num-b=37|num-a=39}} | {{AHSME 50p box|year=1951|num-b=37|num-a=39}} | ||
Latest revision as of 00:01, 9 January 2017
Problem
A rise of 
feet is required to get a railroad line over a mountain. The grade can be kept down by lengthening the track and curving it around the mountain peak. The additional length of track required to reduce the grade from 
to 
is approximately:
Solution
A grade is the rise divided by the horizontal length for a given segment of track. This means we can get the horizontal length of the track by dividing the rise by the grade.
At a grade, the horizontal track length is 
feet. At a grade, the horizontal track length is 
feet. The difference is 
feet of horizontal track. Compared to , feet is insignificant and can be safely covered by the problem's use of the word "approximately." Therefore, the answer is 
.
See Also
| 1951 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 37 |
Followed by Problem 39 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
