What is the maximum distance I can cover assuming changing of wheels is not an issue?

Question

Like an usual car, my new i10 car has 5 wheels(2 front + 2 Rear + 1 spare).
The rear wheel of the car will wear out after 21000 kilometers and the front wheel will wear out after 29000 kilometers.

What is the maximum distance I can cover assuming changing of wheels is not an issue?

Answer 1

Maximum distance: 30,450 kilometers.

For every 5 kilometers driven using this rotation, each tire will lose (2/29000)+(2/21000) of its tread.So, suppose we drive 5*N kilometers like this. Then, each tire will lose 2*N*((1/29000)+(1/21000)) of its tread. We wish to determine N so that the latter expression gets to be 1, representing all of each tire's tread. That happens when N=6090, which is when 5*N (the total kilometers were driven) is 30,450.