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Car wheels

Posted on: March 30th, 2014 by

A car has 4 tires and 1 spare tire. Each tire can travel a maximum distance of 20000 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) unlimited number of times.

- via Gpuzzles

2 Responses to Car wheels

  1. superman had this to say about that:

    25k miles.

    Start with tires 1-4 in use, tire 5 as spare. For the first x miles, use 5 as spare. For the next x miles use 4 as the spare, for the next x, use 3 as the spare, then 2, then 1. Each tire has driven 20k miles each, the car has travelled 25k miles.

    This is also optimal because, when the car can no longer proceed, it has to be the case that all tires have worn out. This can be shown by induction. The statement being: Given a strategy in which n tires have worn out by the end (n being 1,2,3 or 4), you can modify the strategy to have n+1 tires wear out at the end and extend the range.

  2. Sid Hollander had this to say about that:

    25000 miles.

    I thought of the problem a s a unicycle with 4 spares. If you rotate the 5 tires per mile traveled at the end of 1 mile you would have used up .8 miles of the 20000 mile (L)ife of each tire.
    After L(ife) miles you use (L *.8)/20000
    When is L Max? When
    (L *.8)/20000= 1
    L= 25000

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