How do I calculate real-life distance using a map scale?

How do I calculate real-life distance using a map scale?

I'm stuck on a homework problem and I think I'm overthinking it. The question is:

A map has a scale of 1cm : 10km. If the distance between two towns on the map is 5.5cm, what is the real-life distance between them?

I'm not sure if I'm supposed to set up a ratio or just multiply. Can someone walk me through the steps? I want to understand the method, not just get the answer.

Applied Mathematics
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3 Answers

Hi @Leo_Petrov, you're right, it's a straightforward multiplication problem once you understand what the scale means. Here's the simplest way to think about it:

The map scale 1cm : 10km is a conversion factor. It means "for every 1 centimeter on the map, it represents 10 kilometers in real life."

So, if you have a distance of 5.5cm on the map, you just need to multiply that by the scale factor:

Real Distance = (Map Distance) x (Scale Factor)
Real Distance = 5.5 cm * 10 km/cm

Notice how the 'cm' units cancel out, leaving you with 'km'.

Real Distance = 5.5 * 10 km
Real Distance = 55 km

So the two towns are 55 kilometers apart in real life.

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Thank you @Anja_Klausen! Seeing it laid out like that with the units canceling makes it click. I was definitely overthinking it. This is super clear.

While direct multiplication works for this problem, it's also helpful to know how to set it up as a proportion. This method is more versatile for complex problems.

You can set up two fractions (a ratio) and make them equal to each other:

(Map Distance 1 / Real Distance 1) = (Map Distance 2 / Real Distance 2)

Plug in your known values:

(1 cm / 10 km) = (5.5 cm / x km)

Now you can cross-multiply:

1 * x = 10 * 5.5
x = 55

So, the real distance (x) is 55 km. This method is really useful when you're given the real distance and need to find the map distance.

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The other answers are spot on. One piece of advice for the future: always pay close attention to the units.

In this problem, the scale is conveniently given as cm to km. Sometimes, a map scale will be given as a unitless ratio, like 1 : 100,000. This means 1 unit on the map is 100,000 of the *same unit* in real life. So, 1 cm on the map would equal 100,000 cm in reality, which you would then need to convert to kilometers (by dividing by 100,000) to get 1 km.

Your problem is simpler, but it's a good habit to always check if you need to do a unit conversion.

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