gas mileage calculations

turbodog · Oct 18, 2005

I'm considering a 2nd vehicle for the bazillion miles I drive each day.

Right now, I get 13.5 mpg. The thing I'm looking at gets about 60. That's a difference of 46.5 mpg.

The purchase price of my "toy" would be $6000, and I drive about 20,000 miles per year. I would keep my existing vehicle also.

So I decide I'll figure up how many miles I will drive with the new thing before I save the $6000 purchase price. I am ignoring insurance/title/etc.

First I decide that I'll take X miles, divided by the difference in fuel mileage (46.5) times $3 per gallon (easy number to deal with). This should equal $6000. Like so: X/46.5*3=6000. That gives 90,000 or so for X. This sounds high.

I look at it this way, 20,000 miles/year @ 13.5 mpg and $3 gas is $4444 per year. The same 20,000 miles @ 60mpg is $1000. This is a yearly savings of $3444 or $287/month. $6000/$287 is about 21 months or 35,000 miles.

I came up with this equation finally:
(x/13.5-x/60) * 3 = $6000. This gives the correct mileage of 35,000 miles.

Why doesn't the first try work though? In reality I'm saving the DIFFERENCE between 13.5 and 60 mpg. Why is that not the same as 46.5 mpg? Argh! This is too simple. It's like the classic bellboy/hotel puzzle.

270winchester · Oct 18, 2005

The problem is that the difference is not linear, i.e., between 60 and 13.5, if you use x/46.5*3=6000, you are actually deriving a new variable, because you will drive x miles, but x is not the same for 60mpg and 13.5 mpg. So lets say x=20000, cost at 13.5=20000*3/13.5=60000/13.5=4438dolars in expense. at 60 you are using less fuel, so 60000/60=1000 dollars spent in fuel, you have a 3438 in savings, then 6000/3438=1.74, 1.74*20000=34000 miles. You need a constant x for yearly milage as a base.

In your equation, x=miles needed, but by using 46.5, you are actually deriving the cost of fuel for a car with 46.5 mpg gas milage. Not the cost difference of a 60 and a 13.5. With 13.5 and 60, they need to be inverted and the subtracted rather than lenearly subtracted, since 1/60-1/13.5 does not equal 1/(60-13.5)]

for this case, 3/13.5-3/60=.222-.05, where .222 is the dollar of per mile cost of yoru current car, and .05dollar is the cost of your new ride. the difference of that is about 17 cents, and you need 34000 miles to make a 6000 dollar saving.

what you did is 3/46.5=.063 dollar per mile, and the 90000 dolalr figure is the approxiatemate miles that 6000 dollars will get you.

Hope this wasn't too poorly written..

nick

Lynx_Arc · Oct 18, 2005

There is also one other thing to note..... advertised MPG ratings are for highway use on flat roads under more optimized conditions, I tend to take the city mileage as *combined* highway/city milage as you rarely get the high figures they quote unless you live in a noncongested flatland with no traffic lights.

gadget_lover · Oct 18, 2005

turbodog said:
The purchase price of my "toy" would be $6000, and I drive about 20,000 miles per year. I would keep my existing vehicle also.

So I decide I'll figure up how many miles I will drive with the new thing before I save the $6000 purchase price. I am ignoring insurance/title/etc.

You are also ignoring the residual value of the toy. If the toy is worth $4,000 after X miles, you only have to figure out how many miles to pay back $2,000 (the depreciation).

Daniel

turbodog · Oct 18, 2005

Lynx_Arc said:
There is also one other thing to note..... advertised MPG ratings are for highway use on flat roads under more optimized conditions, I tend to take the city mileage as *combined* highway/city milage as you rarely get the high figures they quote unless you live in a noncongested flatland with no traffic lights.

Does it matter that my current vehicle's 13.5 mileage IS the highway rating?

turbodog · Oct 18, 2005

gadget_lover said:
You are also ignoring the residual value of the toy. If the toy is worth $4,000 after X miles, you only have to figure out how many miles to pay back $2,000 (the depreciation).

Daniel

There are no plans to sell it. Only interested right now in how long to break even on the purchase price.

turbodog · Oct 18, 2005

270winchester said:
The problem is that the difference is not linear, i.e., between 60 and 13.5, if you use x/46.5*3=6000, you are actually deriving a new variable, because you will drive x miles, but x is not the same for 60mpg and 13.5 mpg. So lets say x=20000, cost at 13.5=20000*3/13.5=60000/13.5=4438dolars in expense. at 60 you are using less fuel, so 60000/60=1000 dollars spent in fuel, you have a 3438 in savings, then 6000/3438=1.74, 1.74*20000=34000 miles. You need a constant x for yearly milage as a base.

In your equation, x=miles needed, but by using 46.5, you are actually deriving the cost of fuel for a car with 46.5 mpg gas milage. Not the cost difference of a 60 and a 13.5. With 13.5 and 60, they need to be inverted and the subtracted rather than lenearly subtracted, since 1/60-1/13.5 does not equal 1/(60-13.5)]

for this case, 3/13.5-3/60=.222-.05, where .222 is the dollar of per mile cost of yoru current car, and .05dollar is the cost of your new ride. the difference of that is about 17 cents, and you need 34000 miles to make a 6000 dollar saving.

what you did is 3/46.5=.063 dollar per mile, and the 90000 dolalr figure is the approxiatemate miles that 6000 dollars will get you.

Hope this wasn't too poorly written..

nick

I too finally got down to the .22/mi and .05/mi costs.

I think my initial "46.5" error was in reference to the wrong variable. I was thinking that I was looking at the difference in # of miles. That I was actually driving something that got 46.5 mpg. In reality, I guess I would be buying a gallon of gas and then getting to go an extra 46.5 miles over my initial 13.5 miles.

I wonder if there's ANY equation that would still find my answer AND use the 46.5 figure.

jtr1962 · Oct 18, 2005

This is why in most other places they rate fuel economy in liters per 100 km. You can just take the difference between two cars to figure the distance you need to drive to save x amount of money. Let's do your example, only to not be bothered with conversion factors we'll assume the cars are rated in gallons per 100 miles (essentially the same thing as liters per 100 km except different units). 13.5 mpg is 7.41 gallons per 100 miles while 60 mpg is 1.67 gallons per 100 miles. Note how in this case lower is actually better. Take the difference between the two which is 7.41-1.67, or 5.74 gallons per 100 miles. In order to save $6000, which is 2000 gallons of gas at $3/gallon, you need to drive (2000/5.74) * 100 = 34,843 miles. Same answer as you had, but alot easier to figure if the cars had been rated in gallons per 100 miles instead of miles per gallon.

turbodog · Oct 18, 2005

jtr1962 said:
This is why in most other places they rate fuel economy in liters per 100 km. You can just take the difference between two cars to figure the distance you need to drive to save x amount of money. Let's do your example, only to not be bothered with conversion factors we'll assume the cars are rated in gallons per 100 miles (essentially the same thing as liters per 100 km except different units). 13.5 mpg is 7.41 gallons per 100 miles while 60 mpg is 1.67 gallons per 100 miles. Note how in this case lower is actually better. Take the difference between the two which is 7.41-1.67, or 5.74 gallons per 100 miles. In order to save $6000, which is 2000 gallons of gas at $3/gallon, you need to drive (2000/5.74) * 100 = 34,843 miles. Same answer as you had, but alot easier to figure if the cars had been rated in gallons per 100 miles instead of miles per gallon.

That's the way I was sort of thinking of it. I knew how to properly calculate it, but was still trying to get my mind around why 46.5 would not work in some way.

chimo · Oct 18, 2005

I worked this out a few years ago. Note the MPG figure is Imperial and not US Gallons. (I will leave a bit for you to work on

)

Q x N = 283.399

where:

Q = Imperial MPG
N = L/100 km

Paul

DieselDave · Oct 18, 2005

What about the variable of being squashed while driving the 60 MPG toy by someone driving one of those 13.5 MPG rigs or the same by doing battle with a wall or the pavement. Loss of income, hospital bills and so on.

I would love a bike for the fun and MPG but in my situation I can't afford it. The cost of the bike is chump change in my cost analysis, it's the other potential cost that drive it out of my price range.

Be careful

gas mileage calculations

turbodog

Flashaholic

270winchester

Flashlight Enthusiast

Lynx_Arc

Flashaholic

gadget_lover

Flashaholic

turbodog

Flashaholic

turbodog

Flashaholic

turbodog

Flashaholic

jtr1962

Flashaholic

turbodog

Flashaholic

chimo

Flashlight Enthusiast

DieselDave

Super Moderator,

Similar threads

Latest posts