Question

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:

$10{,}000$ ft.

$20{,}000$ ft.

$30{,}000$ ft.

$12{,}000$ ft.

None of these

Answer: A

Concepts:percentage ratio and proportion

Difficulty rating: 1410

Small Hint:

Grade is rise divided by track length

Big Hint:

Compare $\frac{600}{0.03}$ with $\frac{600}{0.02}$

Solution:

A $3\%$ grade requires about $\frac{600}{0.03}=20{,}000$ feet of track, while a $2\%$ grade requires $\frac{600}{0.02}=30{,}000$ feet. The additional length is $10{,}000$ feet.

Thus, the correct answer is A.

1951 AMC 12 Problem 38

Answer: A

Difficulty rating: 1410

Small Hint:

Big Hint:

Solution:

Problem 38 in Other Years