Originally posted by sonhouse
You see the price of petrol going down but its still very differant from place to place. You know about a gas station that has gas cheaper than the one a couple of blocks from home. So make a formula that takes into account the money you save by going to a distant gas station vs. the distance. Obviously if you drive 50 Km to save a couple of pennies per lit ...[text shortened]... pend more for the trip than the savings. So what is the formula for figuring out all such cases?
Let:
S = savings (dollars)
B = base price of petrol (dollars/litre)
C = cheaper price of petrol (dollars/litre)
V = volume of petrol purchased (litres)
d = distance between petrol stations (kilometers)
k = mileage proportionality constant (depends on average speed, car design, car condition, etc...) (kilometers/litre)
Assuming you will do either of the following:
(a) drive an insignificant distance to the base petrol station, purchase enough petrol to completely fill the tank, then drive an insignificant distance home; or
(b) drive some distance "d" to the cheaper petrol station, fill up enough petrol to completely fill the tank, plus purchase enough petrol in a can so that you can fill up the tank completely when you get home, then drive home (same as driving to the base petrol station) and fill up the tank;
Then:
S = B*V - C*(V+2*d/k)
The break-even point occurs when S=0, which gives:
B*V = C*(V+2*d/k)
C = B*V/(V+2*d/k)
Here are some typical values for me:
B = 0.85 dollars/litre
V = 40 L
d = 5 km
k = 9.8 km/L (2002 Ford Taurus)
With these numbers, the break even cheaper price would have to be 0.828 dollar/litre before I would start saving money. But even if the cheaper price were 0.80 dollars/litre, I'd only be saving about $1.18 on a $34 purchase. Probably not worth the hassle of the extra drive and putting in more petrol from a can.