Zigler,
I think I disagree - it's been a long time since I've done math - but this is what I'm thinking:
If I spend C to increase my mileage and my efforts fail, then N and P are equal. My delta mpg goes to zero and by your formula it takes zero miles for payback, when it should go infinite. It will never payback, as my formula correctly predicts.
Looking at it another way (and this is how I derived my formula):
I travel 12000 miles at 17 miles per gallon and gas is 2.95 per gallon, I ‘ve used 706 gallons that cost $2082
(M/P*G in my notation)
I travel 12000 miles at 20 miles per gallon and gas is 2.95 per gallon, I ‘ve used 600 gallons that cost $1770
(M/N*G)
I will have saved $312 at the higher mileage (M/P – M/N)*G= c the cost savings.
When the cost savings (c) and the cost spent (C) are equal that’s my payback mileage. If I spent $312 to go from 17 to 20 mpg, then I break even at 12000 miles.
Shuffling those terms around leads to my equation (I’m sure “shuffling” isn’t allowed in a formal proof but this all for fun.)
Using the lower numbers
I travel 12000 miles at 8 miles per gallon and gas is 2.95 per gallon, I ‘ve used 1500 gallons that cost $4425
I travel 12000 miles at 11 miles per gallon and gas is 2.95 per gallon, I ‘ve used 1091 gallons that cost $3218
I will have saved $1206 at the higher mileage.
The starting point does matter. With these old trucks, many aren’t driven enough to justify an upgrade strictly for mileage. Do the upgrade for fun and this is all moot. Please don’t take offense and feel free to correct me if I’m again wrong.
Thanks,
Chuck
