The problem describes a map scale where 4.5 inches represents 450 miles. You are asked to determine how many miles correspond to 8.5 inches on the map.

We can solve this using a proportion:

$\frac{4.5 \, \text{inches}}{450 \, \text{miles}} = \frac{8.5 \, \text{inches}}{x \, \text{miles}}$

Where $x$ is the distance in miles we need to find. Let's solve for $x$:

$x = \frac{8.5 \times 450}{4.5}$

I'll calculate this.The two cities are 850 miles apart.

Would you like further details or have any questions? Here are five related questions you might explore:

1. How would the distance change if the scale was different (e.g., 3 inches = 450 miles)?
2. How can we convert inches to kilometers instead of miles on this map?
3. What is the formula for scaling distances on a map in general terms?
4. How does this calculation change if the map uses a different unit of measure (e.g., centimeters)?
5. How could we estimate the real-world distance between two cities if the map scale is not provided directly?

Tip: When dealing with map scales, it's important to keep the units consistent. Always check if the scale uses the same units for both measurements.