Final answer:
To find the actual distance between two cities on a map with a scale of 1/4 inch equals 2 miles where the cities are 2 1/4 inches apart, set up a proportion and solve for the distance to find that the actual distance between the cities is 18 miles.
Step-by-step explanation:
The student is asking how to calculate the actual distance between two cities using a map scale. The map's scale is given as 1/4 inch equals 2 miles, and the cities are 2 1/4 inches apart on the map. To find the actual distance, we can use a proportion where the map scale represents a ratio. This ratio is 1/4 inch to 2 miles. Since the cities are 2 1/4 inches apart on the map, we can set up the proportion as follows:
-
- (1/4 inch) / 2 miles = (2 1/4 inches) / x miles
First, convert 2 1/4 inches to an improper fraction so it is easier to work with in the equation:
-
- 2 1/4 inches = 9/4 inches
Now, cross multiply to solve for x (the actual distance in miles):
-
- (1/4) * x = 2 * (9/4)
-
- x = (2 * 9/4) / (1/4)
-
- x = 2 * 9
-
- x = 18 miles
So, the actual distance between the two cities is 18 miles.