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Tread Ware (Posted on 2013-08-20) Difficulty: 3 of 5
Suppose you know that tires on the rear of your car will wear out after 21000 miles, while tires on the front of your car last for 29000 miles. Suppose you have a new car and five identical new tires (four installed and one spare.) What is the maximum distance you can drive, assuming you can easily change the tires any time you want?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 2.5000 (2 votes)

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Solution evolution of a solution Comment 4 of 4 |

Suppose you rotate your tires every 1000 miles, including the spare position in the rotation. After 5000 miles, each tire will have spent 1000 miles in each position.

Each tire will then have lost 2000/29000 of its tread while in front, and 2000/21000 while in the back for a total of 100/609 of its tread.

Theoretically then, this means that the tires could last 5000*609/100 = 30,450 miles. However, at the sixth rotation (30,000 miles after the purchase), only 450 theoretical miles would remain, and the rotation interval would have to be reduced. It would be better to make the rotation interval a better one to begin with rather than keeping readjusting it.

Instead of rotating every 1000 miles, rotate every 1000*609/600 = 1015 miles. Then, after 5075 miles, each tire will have spent 1015 miles in each position.

Each tire will then have lost 2030/29000 of its tread while in front, and 2030/21000 while in the back for a total of 1/6 of its tread. After 6*5075 = 30,450 miles you will have maximized the use of the tires.

Better yet, rotate every 6090 miles; then, once each of the five tires has been in each position for an entire 6090 miles you will have achieved the maximum use of your tires: still that 30,450 miles.


  Posted by Charlie on 2013-08-20 12:18:29
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