1951 AHSME Problems/Problem 38

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 $\boxed{\textbf{(A)}}$ .

1951 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 37	Followed by Problem 39
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1951 AHSME Problems/Problem 38

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