Answer
Fixed cost:
Purchasing the automobile
Insurance
Road tax
Variable cost:
Fuel consumption
Vehicle maintenance
Parking
Costs to consider when traveling inter-state:
By plane:
Variable cost of plane tickets, traveling from home to the airport and from the airport to destination
By car:
Variable costs of fuel consumption, additional insurance, road taxes/tolls, parking
Fixed cost of buying a car (but since the question says "your car", it can be safely assumed that this can be ignored).
Implicit costs should not be ignored in this case, as the opportunity cost of choosing one option is apparent (the other option), and choosing one would mean that the other is not chosen.
Work Step by Step
The considerations are mostly variable costs, as the cost of traveling is, by virtue of having a choice between two that can be made in the short run, variable by design. The ability to change and vary costs within the short run is also part of the business model of such transport companies.
