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.