Car with a Spare Tyre | Puzzle 2

Question

A car has total in all 5 tyres (4 tyres fixed and 1 spare tyre). Each tyre can travel a maximum distance of 20000 miles before wearing off. What is the maximum distance the car can travel before you are forced to buy a new tyre? You are allowed to change the tyres (using the spare tyre) unlimited number of times.

Solution

25000 KMs

Divide the lifetime of spare tire into 4 equal part i.e., 5000 and swap it at each completion of 5000 miles distance.
Let four tyres be A, B, C and D and spare tyre be S.

First of all the cars runs for 5000 KMs with tyres A, B, C and D fixed.

Then after,

5000 KMs: Replace A with S.

10000 KMs: Put A back to its original position and replace B with S

15000 KMs: Put B back to its original position and replace C with S

20000 KMs: Put C back to its original position and replace D with S

Please share your thoughts in the comments.