On a map, 4 inches represent 135 miles. If two cities are 4.5 inches apart on the map, how far are they actually apart? The distance between the cities is $$ \square $$ miles. (Round to the nearest mile as needed.)

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To solve the problem, we need to determine the actual distance between the two cities based on the scale provided on the map.

1. **Identify the scale**: The map scale states that 4 inches represent 135 miles.

2. **Set up a proportion**: We can use the scale to find out how many miles correspond to 4.5 inches. We can set up the following proportion:
   $$
   \frac{4 \text{ inches}}{135 \text{ miles}} = \frac{4.5 \text{ inches}}{x \text{ miles}}
   $$
   where $$ x $$ is the actual distance in miles.

3. **Cross-multiply to solve for $$ x $$**:
   $$
   4 \cdot x = 4.5 \cdot 135
   $$

4. **Calculate $$ 4.5 \cdot 135 $$**:
   $$
   4.5 \cdot 135 = 607.5
   $$

5. **Now, divide both sides by 4** to find $$ x $$:
   $$
   x = \frac{607.5}{4}
   $$

6. **Calculate $$ x $$**:
   $$
   x = 151.875
   $$

7. **Round to the nearest mile**: The distance between the cities is approximately 152 miles.

Thus, the distance between the cities is $$ 152 $$ miles.
The distance between the cities is 152 miles.

On a map, 4 inches represent 135 miles. If two cities are 4.5 inches apart on the map, how far are they actually apart? The distance between the cities is \( \square \) miles. (Round to the nearest mile as needed.)

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