Question/problem for the math wizards

weo

weo

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Sep 21, 2014
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Hello all. I've been trying to figure out what percentage range my vegetable oil/diesel will eventually achieve (and the equation I guess). I figure I could just calculate a few values, but I'm wondering if anyone can tell me the answer.

Here's the question. I run my truck on a combination of vegetable oil (WVO) and diesel. The tank started with a full tank of diesel. After going through 1/3 tank, I fill it with WVO, so we're at 33% WVO, 66% diesel. I run through 1/3 tank and fill it with diesel. Now it gets confusing, I went through 1/3 so where do we go from here? or does that even matter?
I'm repeating this pattern of filling my tank after burning 1/3, alternating between diesel and WVO.

I'm thinking the equation will be something like (1/3)n x 1/3^n where n is the week number?
or is this the equation for if I fill the tank with WVO every time?

Thanks for the help.
 
OK,
Lets say the tank holds 10 gallons. We will ignore the lost tenth and do fast head math.

Week #1 a s 100% deisel.

Week #2 was 33% wvo and 66% deisel. That is 3.3 gallons of wvo and 6.6 galon of deisel.

Week #3 has .66 times 3.3 gallons of wvo. That's 2.2 gallons of wvo left. The deisel is now .66 times 6.6 gallons which is 4.4 gallons, plus the new 3.3 galons. That's 7.7 gallons. So, week #3 is 22% wvo and 77% deisel.

Week #4 is .66 times 7.7 of deisel = 5.1 gallons of deisel. The wvo is .66 times 2.2 = 1.5 gallons plus the new 3.3 gallons. That is 4.8 gallons. So, week #4 is 51% deisel and 48% wvo.

Week #5 is .66×5.1=3.4+3.3=6.7 deisel and .66×4.8=3.2 wvo ...67%, 32%.

Use the same formula to calculate each week.
 
Last edited:
Thanks, Stacy. I did the same thing, only using 100 gal. I'm still curious about what the equation would be.
 
There was a time when I would spend a couple hours writing that equation, but now I waste my time making knives. It would be a bit complex because the vaiables change every week, and there are more than two variables.
 
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