The issue of being prepared by carrying a spare is important as JoeDS points out above Most any service truck will be able to change a tire for you but Billy Bob in Mayberry may have to send to the big city to find one for you ... add two days to your trip.
Also, before deciding to be prepared to change a tire on the road I went to a tire service store and paid to have my tires rotated. Be sure it's a place where you can WATCH them work ... you will learn something if not already experienced.
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