A fuel economy riddle...with a moral to the story
 

A married couple have 2 vehicles, both powered by gas.

The husband has an antique truck that gets 10 mpg.

The wife has a hyper fuel efficient car of the future that gets 100 mpg.

Both drive the same 12,000 miles per year.

They both need to cut back on fuel costs, so they go to a mechanic to ask him to help them save some fuel.

The husband is told that if he cleans the crud from bird droppings off his roof and inflates his tires to recommended PSi instead of being nearly flat, he will get 11 mpg from his truck.

The wife takes her vehicle to the dealer and the dealer says they have a hyper efficient chrome plated caneuter valve that will double her mileage so she gets 200 MPG!!!

Who will save more money?

Lol, the wife, because she is burning 1031 gallons less a year than her husband ;)

Sorry, for the sake of the story, it's whomever is saving more money compared to their old MPG figures. Sure she is using a fraction of his fuel, but she can't haul stuff around in her econobox like he does.

lol, I'm just messin. I am a little concerned that there's a moral involved with this hypothetical though :)

She could get the job done with a trailer or a rental, but let's suppose he's a lumberjack by trade and he likes to take his work home with him. Or maybe he's just really stubborn.

He'll actually save more gas just by inflating his tires properly than she'd save by replacing all her bodywork with dry carbon fiber, installing movable aerodynamic devices, getting manual control of her electric motors, and developing that $3000 thermoelectric exhaust waste heat recovery system that she would love to use to charge her traction battery.

My boss wastes far more fuel by accidentally bumping his remote starter button (once a week, it seems) than I save by having a car without A/C. Or, for that matter, than I would save with a boat-tail.

Look at the gal/mi data before buying a car. It's a more relevant way that makes this riddle very obvious.

He burns 10 gal per hundred miles. She burns 1. He would go to 9gal/100mi, and she would go to .5gal/100mi.

He would because the mod are free.

This got me thinking about the claim made by Mobil that their Mobil-1 0W-30 could potentially increase mileage by 2% over conventional 5W-30. I was standing in the store thinking, "Hmmmm. 2% isn't very much. But I'm already getting 35 MPG by ecodriving my car. So 2% on top of that is much better than 2% on top of the EPA estimated 21 that my car is rated at." On the surface it sounds like the more fuel efficient your car is, the more this oil could potentially save you. The reality is actually not as bright.

The better your FE, the less money you will save.

not sure you did that right. it isn't at all obvious when fuel is in the denominator so lets flip it.

in your scenario car A(10mpg) gets .1 gpm (gallons/mile)
and car B(20mpg) gets .05 gpm.

so @ 10k miles a year they would use 1000 and 500 gallons respectively.

so 2% of that would be ~20 gallons and 10 gallons respectively "saved per year".

The other "gamey" aspect of this is that the fuel returns seem to taper off as gallons used approaches zero.

If you were to assume we had, say, rations of fuel (it's happened before), where you only get 500 gallons a year and were to look at how many miles you could travel on that allotment with different cars it puts a different spin on things.

@ 500 gallons/year

a .1gpm car could go 5000 miles
a .05gpm car could go 10000 miles
a .025gpm car could go 20000 miles

so in each case we decreased consumption by 50% and doubled the range.

Pickup guy went from 1200 gallons of fuel per year to 1090.91 gallons, saving 109.09 gallons of fuel. Hyper efficient wife went from 120 gallons of fuel to 60 gallons, saving 60 gallons.

Now if she could convince him to drive an efficient car to drive to work and back and keep his pickup truck for cruise nights with the car club guys, the savings could pay for that new paint job he's probably dreaming about.