Question

Your car has 4 tires and 1 spare tire. Each tire can travel at most 10,000 miles before wearing off. What is the maximum distance the car can travel before you are forced to buy a new tire? You are allowed to change tires (using the spare tire) an unlimited number of times.

• A. 10,000 miles
• B. 12,500 miles
• C. 15,000 miles
• D. 17,500 miles

Answer 1

The correct option is B 12,500 miles

Let the regular tires be A, B, C, and D, and the spare tire be S.

In the beginning, we have the life of each tire as:


After 2,500 miles, we switch tire A with the spare tire S:


After 5,000 miles, we put tire A back in its position and switch tire B with the spare tire S:


After 7,500 miles, we put tire B back in its position and switch tire C with the spare tire S:


After 10,000 miles, we put tire C back in its position and switch tire D with the spare tire S:


Finally, after 12,500 miles, we have the life of each tire as:


Hence, on the given tires, the car can travel a maximum distance of 12,500 miles before a new tire is required.