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A road map has a scale of 1: 50000. The length of the road on the map is 8.5cm. Work out the length of the real road in km

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Answer:

2.74 miles

Explanation:

The road map scale says that 1 cm represents 50,000 cm in real life.

That's a conversion factor: 1cm map/50000cm actual from map to actual

But we want to know a conversion factor that would convert map cm to miles actual. [cm map/actual miles]

Let's start with what we know:

(1cm map)/(50000cm actual)

Now lets find a factor that will allow us to convert cm to miles:

We could start by finding the conversion factor for cm to inch, then knowing there are 12 inches/foot, and 5200 feet/mile and calculate the conversion from 1 cm to miles. Instead, I'll use a reference value:

1 cm = 6.2137x10^-6 mi

Now we can find the conversion factor in miles:

1 cm = 6.2137x10^-6 mi

or 1 = [1cm/(6.2137x10^-6 mi)]

Now do the conversion:

[(1cm map)/(50000cm actual)[*[1cm actual/(6.2137x10^-6 miles)]

[(1cm map)/(50000)[*[1/(6.2137x10^-6 miles)] [cm actual cancels, leaves miles]

[(1cm map)/[(50000)*(6.2137x10^-6 miles)]

1 cm map/0.311 miles

or we can write this as (0.322 miles/cm map), a conversion factor.

8.5 cm map is therefore = (8.5 cm map)*(0.322 miles/cm map)

8.5 cm on the map is equal to 2.74 miles actual.

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