Question

In model trains, O scale means the models are made using a 1:48 scale. In the U.S., real train tracks have rails that are 4 ft 8 in apart.

a. If miniature train track was made using O scale, how far apart should the rails be? Round to the nearest hundredth of an inch.

b. The word gauge refers to how far apart the model rails are. For some reason, O gauge track does not exactly use O scale, and O gauge rails are 1.25 inches apart. Find the relative difference of the rail spacing on O gauge track compared to what it should be if it followed O scale. Round to the nearest tenth of a percent.

Answer 1

Part A:

Given that train tracks have rails that are 4 ft 8 in apart.

Converting 4ft 8in to inches, we have 4 x 12 + 8 = 48 + 8 = 56 inches.

Given that the O scale models are made using a 1:48 scale, let the distance apart of the miniature train track made using the O scale be x, then

$\frac{1}{48} = \frac{x}{56} \\ \\ \Rightarrow x= \frac{56}{48} =1.67$

Therefore, the miniature train track made using the O scale is 1.67 inches apart.



Part B:

Given tha the O guage rails are 1.25 inches apart whereas it was supposed to be 1.67 inches apart.

The relative difference of the rail spacing on O guage track compaired to what it should be if it followed the O scale is given by

$\frac{1.67-1.25}{1.67} \times 100\%= \frac{0.42}{1.67} \times 100\%=0.251\times100\%=25.1\%$