Final answer:
To determine the actual distance between two towns that are 2 3/4 inches apart on a map with a scale where 1/4 inch represents 16 miles, you multiply the number of 1/4 inches in 2 3/4 inches by 16. This results in the towns being 176 miles apart.
Step-by-step explanation:
To find out how many actual miles are represented by 2 3/4 inches on the map, we can set up a proportion based on the given scale. Here, 1/4 inch equals 16 actual miles.
First, let's calculate how many times 1/4 is contained in 2 3/4 inches. Since 2 3/4 can be written as 11/4 (because 2 equals 8/4 and 8/4 plus 3/4 equals 11/4), we find that 1/4 inch goes into 11/4 inches exactly 11 times.
Now, we multiply the 11 by the number of actual miles that 1/4 inch represents:
- Multiply the number of times by the miles each 1/4 inch represents: 11 × 16 miles = 176 miles.
Therefore, the two towns that are 2 3/4 inches apart on the map are actually 176 miles apart.