Final answer:
The scale of a map that shows a 400-mile distance as 2.5 inches apart is calculated by dividing the real distance by the map distance, resulting in a scale of 1 inch = 160 miles.
Step-by-step explanation:
Understanding Map Scale
To determine the scale on a map that shows two cities 400 miles apart as 2.5 inches apart, you must establish a proportion based on the given distances. Scale is essentially a ratio that compares a distance on the map to the actual distance it represents in reality. The scale for this situation can be found through setting up a proportion that compares map inches to real-world miles.
To calculate the scale, divide the real distance (400 miles) by the map distance (2.5 inches). This provides us with the scale ratio which can be expressed as 'x inches = 1 mile' where 'x' is the value obtained from our calculation. From here, you can use the scale to convert other map distances to real-world distances or vice versa.
For example:
- If 2.5 inches on the map equals 400 miles, then 1 inch would represent 160 miles in the real world. So, the scale of the map would be 1 inch = 160 miles.
This scale can then be used for other calculations on the map. If you have another distance on the map in inches, you simply multiply it by 160 miles to find out how far it represents in the real world.