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Re: actually....
Posted by Ted Yurkon [Email] (more from Ted Yurkon) on Fri, 31 Aug 2007 17:00:27
In Reply to: actually...., markP, Thu, 30 Aug 2007 11:19:09
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Quite right, but I had to know for sure. Here it is:
If your current Tank octane is T0 at half tank, and you fill up once with 93, then with 87 at half tanks, it doesn't take much to figure that you'll end up at
T1 = T0/4 + 93/4 + 87/2 = (T0+267)/4
Extending this logic to tank n,
Tn = (T0+267)/4^n + 267/4^(n-1) + ... + 267/4^1 [^ means raised to the power]
Thus,
4Tn = (T0+267)/4^(n-1) + 267/4^n + ... + 267/4^0,
and
4Tn-Tn = 3Tn = (3T0+801)/4^n + 267/4^n + 267 [all other terms cancel].
This reduces to:
Tn = (T0+356)/4^n + 89
as the tank octane after the nth cycle of 93 and 87.
As n approaches infinity, the first term approaches zero, and Tn approaches 89.
The intermediate tanks will of course approach 91.
Now I'm happy :-)
PS: I only use 93 because 93=93=93=93...
posted by 76.190.23...
Posts in this Thread:
- Gas...prem vs. reg, tk505, Tue, 28 Aug 2007 20:06:09
- Required, recommended and controversial....., Mike Lynch
, Fri, 31 Aug 2007 11:43:02 - Re: Gas...prem vs. reg, Ozzie, Wed, 29 Aug 2007 05:58:27
- Salesman was wrong....., MI-Roger
, Wed, 29 Aug 2007 05:32:18
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