Friday, February 13, 2009

Using Real-World Algebra to Establish a Real-World Delusion

Well, I filled my fuel tank for the second time since replacing the engine. The first fill-up was right after I took delivery, so it really doesn't count. Now that I have driven the new engine around for nearly a week, I finally have my first inkling of how it's doing on fuel economy.

The result? A fantastic 38 mpg!

Well, given how much the repair cost, I've been looking for the bright side, and here's how I found it:

I took the initial mileage with the new engine and compared it to the recent mileage of the old engine, and assumed (falsely, of course) that the difference will be constant. Then I built an algebraic equation to suit my whims, and determined that the new engine will pay for itself. Specifically, if we assume that the average price of gas will be $2 per gallon, it will pay for itself over the course of 194,746 miles. At an average of $3 per gallon, it will pay for itself over the course of 129,831 miles. And if we assume that the average price of a gallon of gas over the next several years will be $4, it will pay for itself in just 97,373 miles.

Hooray for algebra!

In case you're wondering, here's the equation:

price per gallon(x/old mpg)-price per gallon(x/new mpg)=installed price of replacement engine

Solve for x and suddenly I feel like a winner!

So, to all of you who've said "algebra is useless in the real world", I say "HA!"

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