You can put this solution on YOUR website!
5.5 inches represent 198 miles so
1 inch represents 198/5.5 miles = 36 miles
1 inch represents 36 * 5280 feet = 190080 feet
1 inch represents 190080 * 12 inches = 2280960 inches
So the map scale is 1:2280960
You should know whether this is the type of answer you are after or if one of the intermediate values is more what you were looking for.