Final answer:
To calculate the actual distance between two towns on a map, convert the map distance to decimal, establish a proportion using the map scale, solve for the unknown distance, and calculate the result to find the actual distance in miles.
Step-by-step explanation:
To find the actual distance between two towns that are 2 1/4 inches apart on a map, we need to know the scale of the map. Unfortunately, the scale isn't provided in the question. Let's assume the scale given is similar to the examples provided, such as 1/4 inch = 43 miles.
First, convert 2 1/4 inches to a decimal by multiplying 2 by 4, adding 1 (for the 1/4) which equals 9, and then dividing by 4. This gives us 2.25 inches. Then set up a proportion:
1/4 inch / 43 miles = 2.25 inches / X miles
Solving for X gives us the actual distance. Multiply both sides of the proportion by the actual distance X to find the cross products:
2.25 inches * 43 miles = 1/4 inch * X
Then, multiply 2.25 by 43 to find the number of miles that 2.25 inches represents:
X = (2.25 * 43) / (1/4)
Calculate the result to find X, which represents the actual distance in miles.