Winter tires and treads

Algebra Level pending

Jolene bought 4 brand new winter tires for her car.

That particular brand can last for 20000 km on the front wheels and for 30000 km on the rear wheels.

By interchanging the front and rear tires, what is the greatest distance that Jolene can get from the set of tires?


The answer is 24000.

Paul Fournier by Paul Fournier , 70, Canada

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1 solution

Paul Fournier
Oct 16, 2015
  1. Let us say you have 1 unit of thread thickness per tire.
  2. You lose 1/20000 unit per km when the tire is on the front wheels and 1/30000 unit per km when the tire is on the rear wheels.
  3. So every km you lose 1/20000+1/20000+1/30000+1/30000=1/6000 unit.
  4. This lost can be distributed on the four tires.
  5. 1/6000 divided by 4 gives 1/24000.
  6. Thus one should be able to get 24000 km by rotating the tires.
  7. One solution is switching the tires at 12000 km.
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Moderator note:

Simple standard approach. Thanks for pointing out how this upper bound can be achieved.

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