A car has 4 tyres 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 tyres (using the spare tyre) unlimited number of times.
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.
5000 KMs: Replace A with S. Remaining distances (A,B,C,D,S) : 15000,15000,15000,15000,20000
10000 KMs: Put A back to its original position and replace B with S. Remaining distances (A,B,C,D,S) : 15000,10000,10000,10000,15000
15000 KMs: Put B back to its original position and replace C with S. Remaining distances (A,B,C,D,S) : 10000,10000,5000,5000,10000
20000 KMs: Put C back to its original position and replace D with S. Remaining distances (A,B,C,D,S) : 5000,5000,5000,0,5000
25000 KMs : Every tyre is now worn out completely.
All tyres are used upto their full strength.
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