A car is equipped with 4 tires and 1 spare tire.
- Each tire can last for a maximum of 20,000 km before it wears out.
- You may swap tires 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 tire?
Check if you were right - full answer with solution below.
Answer: 25000 kms
Solution: Divide the lifetime of the spare tire into 4 equal parts, i.e., 5000 km, 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 km: 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 tire is now worn out completely.
All tires are used to their full strength.
