To determine the actual distance between two cities based on the scale provided on the map, we can follow these steps:
1. Identify the scale: The problem states that the scale on the map is 1 inch = 100 miles. This means for every inch measured on the map, the actual distance corresponds to 100 miles.
2. Measure the distance on the map: The distance between the two cities on the map is given as 5.5 inches.
3. Calculate the actual distance: To find out the actual distance in miles, multiply the distance on the map by the scale factor.
[tex]\[
\text{Actual Distance} = \text{Distance on Map} \times \text{Scale Factor}
\][/tex]
Substituting the given values:
[tex]\[
\text{Actual Distance} = 5.5\, \text{inches} \times 100\, \text{miles/inch}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Actual Distance} = 5.5 \times 100 = 550\, \text{miles}
\][/tex]
So, the actual distance between the two cities is [tex]\(550\)[/tex] miles.
Hence, the correct answer is:
[tex]\[
\boxed{550\, \text{mi}}
\][/tex]
