Math CentralQuandaries & Queries


Question from Shelly, a student:

Lindy is planning to build a model of a train using a scale where 2 inches represents 25ft. If the train is 60 feet long, what is the length in inches that Lindy should build the model of the train?

I tried solving this, but I don't know how. Please explain =[


The first thing I do is make an estimate so that when I do the problem precisely I know approximately what to expect.

2 inches represents 25 feet so
4 inches represents 50 feet and
1 inch represents 12.5 feet

Hence 5 inches represents 62.5 feet and thus the correct answer is a little less than 5 inches.

To get from "2 inches represents 25 feet" to "1 inch represents 12.5 feet" I divided both numbers by 2. What if I divide both numbers by 25?

2 inches represents 25 feet so
2/25 inches represents 1 foot. Thus

(2/25) × 60 inches represents 60 feet.

I hope this helps,


Hi Shelly. A scale can be thought of as a fraction. So for the scale 2 inches: 25 feet, that is the fraction 2/25.

When "building to scale" you want to use the same ratio for all the parts.

Therefore, the question is asking you for an equivalent fraction with ?/60. Let me show you how to solve it using a different number. Let's say the engine is 20 feet long. So I will try to find the equivalent fraction for ?/20.

To transform fractions from one denominator to a different denominator, you just have to remember that whatever you do to the bottom, you must do to the top.

So I divide 20 by 25 and I get 0.8. That means that by multiplying the 25 by 0.8, I get 20. So to see what the 2 becomes, I have to multiply it by 0.8 as well.

2 x 0.8 = 1.6.

So the model engine needs to be 1.6 inches long.

Now you try it for a 60 foot length.

Stephen La Rocque.

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