Question

On a map, two cities are 2 1/4 inches apart. The scales of the map is 1/4 inch = 2 miles. What is the actual distance between the towns?

Answer 1

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:

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• (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:

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• 2 1/4 inches = 9/4 inches

Now, cross multiply to solve for x (the actual distance in miles):

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• (1/4) * x = 2 * (9/4)
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• x = (2 * 9/4) / (1/4)
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• x = 2 * 9
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• x = 18 miles

So, the actual distance between the two cities is 18 miles.