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Difference between revisions of "1951 AHSME Problems/Problem 38"

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==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==
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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 $600$ 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 $3\%$ to $2\%$ is approximately:

$\textbf{(A)}\ 10000\text{ ft.}\qquad\textbf{(B)}\ 20000\text{ ft.}\qquad\textbf{(C)}\ 30000\text{ ft.}\qquad\textbf{(D)}\ 12000\text{ ft.}\qquad\textbf{(E)}\ \text{none of these}$

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 $3\%$ grade, the horizontal track length is $20000$ feet. At a $2\%$ grade, the horizontal track length is $30000$ feet. The difference is $10000$ feet of horizontal track. Compared to $10000$, $600$ feet is insignificant and can be safely covered by the problem's use of the word "approximately." Therefore, the answer is $\boxed{\textbf{(A)}}$.

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

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