Puzzle | Car Wheel Puzzle

A car is equipped with 4 tyres and 1 spare tyre.

• Each tyre can last for a maximum of 20,000 km before it wears out.
• You may swap tyres with the spare as many times as you want during the journey.

What is the maximum distance the car can travel before buying a new tyre?

Check if you were right - full answer with solution below.

Answer: 25000 kms

Solution: Divide the lifetime of the spare tyre into 4 equal part i.e., 5000 and swap it at each completion of 5000 km distance. 
Let four tyres be named as 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 to their full strength.