The ten-cent gas station that costs you eight dollars

The question

The station by the highway exit charges ten cents a gallon more than the one on the far side of town. Do you drive over there?

The Dad Math

This is the version done standing in the driveway. Keys are already in hand. The face is the face of a man who has outsmarted an oil company.

• Tank holds 15 gallons. (Example.)
• 15 gallons × $0.10 = $1.50 saved.
• I fill up once a week, so $1.50 × 52 = $78 a year.
• Over thirty years of driving, that's $2,340. That's a riding mower. Possibly a small boat.
• Time cost: zero, because I enjoy driving.
• Conclusion: everybody get in the car.

I ran exactly this math one Saturday. My daughter, nine, asked from the back seat why we'd just passed three gas stations. I told her it was a lesson in money. She said it seemed more like a lesson in gas stations.

She was closer.

The real math

Swap every number below for your own. They're worked examples, not quoted prices.

Step 1: The gas you actually buy. Nobody pulls in on fumes. If you arrive with a few gallons left, you're buying maybe 12 of those 15.

12 × $0.10 = $1.20 saved.

The riding mower just shrank to a nice rake.

Step 2: The fuel the detour burns. Say the cheap station adds 10 miles round trip compared with the one already on your route. The car gets 25 mpg and gas is $3.50 a gallon. Both are examples.

• 10 miles ÷ 25 mpg = 0.4 gallons
• 0.4 × $3.50 = $1.40 in fuel

Stop right there. You've already spent 20 cents more than you saved. And you spent it on gas, which is the exact thing you were trying to buy less of.

Step 3: Wear on the car. Tires, oil changes, brakes and depreciation all run on miles. Fuel is only one line of what a mile costs you, the same trap covered in The car payment isn't the price. Use an example of 15 cents a mile beyond fuel. To find your own figure, add up last year's maintenance, tires and lost resale value, then divide by the miles you drove.

10 × $0.15 = $1.50

Step 4: Your time. The detour, the red lights, the guy at pump four vacuuming out his entire truck cab. Call it 20 minutes. Value your time at an example $20 an hour. Nobody has to be paying you for it. It's a Saturday hour you don't get back, and there's a kid at home who wanted help with a bike chain.

20 ÷ 60 × $20 = $6.67

Step 5: The stuff that only happens to you. You arrive and the line is six cars deep, because every dad in the county saw the same sign. Or the near station dropped its price while you were gone. Or you went inside for "just a water" and came out with jerky, two sodas and a phone charger you already own. None of it is counted below. You know it's real.

The tally:

• Saved: $1.20
• Fuel: $1.40
• Wear: $1.50
• Time: $6.67
• Net: about $8.37 in the hole.

Now be generous. Say your time is worth nothing and you love the drive. Fuel plus wear is still $2.90 against $1.20 saved. That's a loss of $1.70 a week, every week, for thirty years.

Congratulations. You've bought the riding mower for the oil company.

The verdict

Here's the formula. It fits on a gas receipt, so you can run it in the parking lot:

Most extra miles worth driving = (gallons you'll buy × price gap) ÷ (gas price ÷ mpg + other cost per mile)

With the examples above, that's $1.20 ÷ ($0.14 + $0.15). It comes to about 4 extra miles round trip, or 2 miles each way. That figure counts your time as free. Put any value on your time and the number heads toward zero.

The rule of thumb for an ordinary car on an ordinary fill-up: every 10 cents of price gap is worth about 4 extra round-trip miles. A dime justifies a two-mile hop. It doesn't justify crossing town.

Trucks do the same dance. Say you buy 24 gallons at 15 mpg, with wear at an example 20 cents a mile. The savings is $2.40 against about 43 cents a mile, which works out to roughly 5 or 6 miles. The bigger tank helps you. The thirstier engine takes most of it back.

When it's genuinely worth it:

• It's already on your route. Zero extra miles means every cent of the gap is profit. My wife suggested the station across from the grocery store we were going to anyway. She'd done the math without a receipt. She was right, and I've stopped pretending otherwise.
• The gap is big. At 40 cents on 12 gallons, you'd save $4.80. That pays for about 16 extra round-trip miles before time. Now you can talk.
• Warehouse club pumps. The gap there is often wider. Divide the membership fee across your fill-ups first, and count the line.

One thing that isn't a joke. Don't run the tank close to empty to hold out for the cheap station. Running dry on a highway shoulder or in a dark parking lot is a safety problem, not a money one. Fill up when you need to, wherever you are.

If you want to actually save on gas this week, the boring moves win. Check your tire pressure against the sticker inside the driver's door, not the number on the tire sidewall, which is the maximum and not the target. Ease off hard starts. Stack errands into one loop. None of it makes for a good story at dinner, and all of it beats the cross-town run.

Want to try this on the mower, the boat or the pressure washer? Plug your own numbers into the BRO cost-per-use calculator. Better yet, hand the formula to your kids and let them check your work. It's a cheap way to teach your kids money before an app does it for you.

This is general education, not financial advice. Your car, your prices and your time are your own numbers.

My daughter ran the formula on the back of a receipt last weekend. She now believes I owe her $8.37. She also believes I owe her for the jerky.

She's not wrong.