Each of a certain type of tire on a 4 wheel car lasts exactly 10,000 miles. how many spare tires of this same variety must carried so that a trip of 15,000 miles can just be completed.

3 spare tires are needed. This works if you rotate the tires every 5,000 miles. 

Tire A, B, C, D (and spare is E F G)
first 5,000 miles you use tire A B C D
second 5000 miles you use tire B C D E
third 5000 miles you use A E F G

Each tires is used no more than twice (10,000 miles).

No because if you do the higher number minus the lower number you will get a positive. if you do it the other way around you will get a negative number