To solve this problem, we need to use the concept of ratios, based on the given scale of the map.

The scale given is:

• 4.5 inches corresponds to 425 miles.

We need to find the actual distance corresponding to 11.25 inches on the map. Let $x$ be the actual distance in miles.

We can set up a proportion:

$\frac{4.5 \text{ inches}}{425 \text{ miles}} = \frac{11.25 \text{ inches}}{x \text{ miles}}$

Now, solve for $x$:

$x = \frac{11.25 \times 425}{4.5}$

Calculating this:

$x = \frac{4781.25}{4.5} \approx 1062.5 \text{ miles}$

So, the two cities are approximately 1062.5 miles apart.

Would you like further details or have any questions about this solution?

Here are five related questions for practice:

1. If the scale was 3 inches to 200 miles, how far would 7.5 inches represent?
2. What would be the scale if 6 inches on the map corresponded to 600 miles in reality?
3. How many miles would 15 inches on the map represent if the scale was 5 inches to 300 miles?
4. If the actual distance between two cities is 850 miles, how far apart would they be on the map if the scale is 1 inch to 150 miles?
5. If 2.5 inches on the map corresponds to 275 miles, how many miles would 12 inches represent?

Tip: Always double-check your setup when working with proportions to ensure you're relating the correct units to each other.