A cellular service provider is expanding the number of cell towers it has in Wayne County. On a map of the towers, there are two that are 12 inches away from each other. The distance, in real life, is 14 miles. What is the scale of the map?
To find the scale of the map, we need to calculate the ratio of the distance on the map to the distance in real life.
Let's assume that the distance on the map is represented by 'd' inches.
According to the information given, on the map, a distance of 'd' inches represents a distance of 14 miles in real life.
We can set up the following equation:
d inches / 12 inches = 14 miles
To find 'd', we can cross-multiply and solve for 'd':
d = (12 inches * 14 miles) / 1 = 168 inches
Therefore, the distance on the map that represents 14 miles is 168 inches.
Now, we can find the scale by dividing the distance on the map by the distance in real life:
Scale = distance on the map / distance in real life
Scale = 168 inches / 14 miles
Since we want the scale to be in miles per inch, we convert inches to miles by dividing by 63360 inches/mile:
Scale = (168 inches / 14 miles) / (63360 inches/mile)
Scale = 0.1667 miles/inch
Therefore, the scale of the map is approximately 0.1667 miles per inch.