Gasoline Experiment, Part 2

Okay.  Just filled my tank again.  The news is not encouraging.  The MPG this time around was only 33.56.  A bit disappointing compared to what Shell gas did for my car last time.  Well, we shall see how this second tank comes out before making any decisions.  After all, when I had 2 tanks of Shell followed by 1 of generic, I got 39 MPG.

Seeing the $23 spent for a tank of gas, however, made me think.  At what price is the Shell gas really a frugal purchase?  To figure this out, I came up with this formula.  Generic bill calculation:  165 miles ÷ 32 MPG = 5.156 gallons of gas; 5.156 gallons x $3.869 per gallon = $19.95 total bill.  Shell price per gallon calculation:  165 miles ÷ 35 MPG = 4.714 gallons of gas; 4.714 gallons x ? per gallon = $19.95 total bill or ? per gallon = $19.95 total ÷ 4.714 gallons = $4.232 per gallon.

Is that mathematically correct?  Let's see, 4.714 gallons x $3.949 = $18.62.  Therefore, at 35 MPG I would pay $18.62 total at shell, but at 32 MPG I would pay $19.95 at the grocery store.  As long as I am getting 35 MPG, I there can be a price difference per gallon of 36.3¢ per gallon.

Using the same formulas, can I figure out how much MPG I need using Shell gas?  $19.95 total ÷ $3.949 per gallon = 5.052 gallons; 165 miles ÷ ? MPG = 5.052 gallons or ? MPG = 165 ÷ 5.052 = 32.66 MPG.  As long as I get 0.66 more MPG using the Shell gas, I should be saving money.

So why did the $23.01 today seem so high?  Had I bought the gas at the generic price, it would have cost me 5.826 gallons x $3.869 per gallon = $22.54.  However, using the generic gas would have been 32 MPG, and I would have needed to buy more gallons (195.5 ÷ 32 = 6.109 gallons x $3.869 per gallon = $23.64).

If all of these numbers are correct, I need to get at least 0.66 MPG more at an 8¢ price difference to make the Shell gas a frugal buy.  If I do, indeed, get 35 MPG using Shell, the price difference can be as high as 36.3¢.  In 3 days, I will buy another tank, and we shall see if these numbers hold up.