1951 AMC 12 Problem 38

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.