## Monday, June 22, 2009

### Tire swap

Your just bought four new tires for your car. Your car manual says that your front tires could last you 25,000 miles. Your back tires 15,000 miles. You are trying to be creative and come up with an idea of switching your front tires with your back tires after driving 10,000 miles. What tires will go bad now? When?

#### 4 comments:

Alin Grin said...

In case you don't swap the tires:
you will have to buy new ones after 15,000 miles while you still have 10,000 miles on the front tires.
in case you swap after 10,000:
To "move" the back tires to the front you have to multiply by the ratio of wear and tear 25,000/15,000=1.666.
1.666 * 5000 = 9000 miles left on these tires.
To "move" the front tires to the back you have to multiply by the ratio of wear and tear 15,000/25,000=0.6.
0.6 * 15,000 = 8000 miles left on these tires.
So the front tire will wear first after 8000 and you are left with 1000 miles on the back tires.
So if the question is, to swap or not to swap? then defently swap to get more mileage out of these tires.

Maria said...

Very cool, Alin!

I had a slightly different reasoning and came up with a slightly different answer, but like in your solution - swapping does make sense and after the swap front tires will still wear first after additional 8,000 + miles.

My reasoning is below. Please feel free to correct me as anyone may be wrong!
Tire wear & tear is
front: 1 / 25,000 per mile
back: 1 / 15,000 per mile

after 10,000 miles we have:
front tires have lived 10,000 / 25,000 of their life = 2 / 5 and still have 3/5 of their life ahead of them;
back tires have lived 10,000 / 25,000 of their life = 2/3 and still have 1/3 of their life ahead of them.

Back tires now swapped and go on a front where they would have wear & tear of 1/25,000 per mile. If they would be new, they would last 25,000 miles, but they only have 1/3 of their life left, so they would last 25,000 * 1/3 = 8,333.33 miles.

Front tires now swapped and go on a back where they would have wear & tear of 1/15,000 per mile. If they would be new, they would last 15,000 miles, but they only have 3/5 of their life left, so they would last 15,000 * 3/5 = 9,000 miles

Alin Grin said...

Yes that is more accurate. 5000*1.6666=8333

Jessica said...

I don't know for sure how to explain it but i got the the tires that you have put on the front that will last only 6450 miles more. Cause you used 67% of them at 10,000 miles while they were on the front

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