A map has a scale of 1 inch represents 10 miles. If two cities are 4.5 inches apart on the map, what is the actual distance between the cities?

If 1 inch represents 10 miles, then 4.5 inches represents 4.5 * 10 = <<4.5*10=45>>45 miles.

Therefore, the actual distance between the cities is 45 miles. Answer: \boxed{45}.