Question

The distance between two cities on a map is 4 - inches. The actual distance between the two cities is 24 miles.
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a. What is the scale used on the map?
b. If the scale on a different map of the same area is - inch = 1 mile, how many inches separate the same two cities?
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Answer 1

Answer

The scale factor is

Explanation

We have to ways to find the scale factor here:

1. Find the unit fraction from inches to miles; in other words, we need to divide the distance between the cities on the map (in inches) by the actual distance between the cities.

We can conclude that the scale factor is

2. Let  be the scale factor.

We know form our problem that 24 miles times the scale factor is equal 4 1/2 inches, so we can set up an equation an solve for :

Just like before, we can conclude that the scale factor is

B.

Answer

6 inches separate the cities on the map

Explanation

We know that our scale factor is 1/4 inch = 1 mile, so we can create a conversion factor to convert 24 miles to inches. Since we need to convert from miles to inches, the denominator of our conversion factor must be 1 mile so we can cancel miles out. Notice that we can also express 1/4 inch as 0.25 inch to simplify our calculations:

We can conclude that if the conversion factor is 1/4 inch = 1 mile, 6 inches separate the cities on the map.

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