On the certain map, 1.5 inches represents a distance of 120 miles. If two cities on this map are 1 foot apart, what is the distance, in miles, between the cities?

Options

A. `180`
B. `480`
C. `960`
D. `1,080`

Answer

To solve the problem, we need to determine the distance between two cities on a map, given the scale of the map. Here are the steps to find the solution:

### Step 1: Understand the Scale of the Map
The problem states that 1.5 inches on the map represents a distance of 120 miles in reality.

### Step 2: Find the Distance Represented by 1 Inch
To find out how many miles are represented by 1 inch on the map, we can set up a proportion based on the given scale:
\[ \text{Distance per inch} = \frac{120 \text{ miles}}{1.5 \text{ inches}} = \frac{120}{1.5} \]
Calculating this gives:
\[ \text{Distance per inch} = 80 \text{ miles} \]

### Step 3: Convert Feet to Inches
Next, we need to convert the distance between the two cities from feet to inches. Since 1 foot is equal to 12 inches, the distance between the two cities is:
\[ 12 \text{ inches} \]

### Step 4: Calculate the Distance in Miles for 12 Inches
Now, we can find the actual distance represented by 12 inches using the distance per inch we calculated earlier:
\[ \text{Distance for 12 inches} = 12 \text{ inches} \times 80 \text{ miles/inch} = 960 \text{ miles} \]

### Conclusion
Thus, the distance between the two cities that are 1 foot apart on the map is:
\[ \text{Distance} = 960 \text{ miles} \]

### Final Answer
The distance between the two cities is **960 miles**.

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