Question

The two front tires of a car are usually considered worn out after covering 25,000 miles, while the rear pair of tires are considered worn out after covering 15,000 miles. That is why drivers move rear tires to the front and vice versa at least once during the tires' lifetime. Assume that all tires' tread wear evenly over the distance based on their location. After how many miles is it reasonable to move the front and rear tires for the first time in order to have all the tires worn out equally? In this case, what would be the maximum distance covered by the set of new tires before they are worn out completely?

Answer 1

Moving the tires after 9,375 Miles

Maximum distance covered by the new tires - 18,750 miles

Explanation:

Optimal distance before tire need moved to get maximum miles is half of the maximum miles

X miles = When tires need moved

`X/25,000 + X/15,000` = 1 where 1 is tire has worn out

`15,000X/375,000 + 25,000X/375,000 = 1`

`40,000X/375,000 => X = 375,000/40,000 = 9,375` miles