Finding Distance given accleration and Standard Gravity.

[Oannes]

Homework Statement

A car has a performance of 10,705 miles per gallon. If the car is given 100 grams of ethanol (Standard Gravity = 0.789) and drive until the fuel runs out, how far with they go in meters?

Homework Equations

Standard Gravity = Density of the Object /Density of Water
Density = mass/ volume
Distance = Rate * Time traveled

The Attempt at a Solution

I solved for the density using the standard gravity formula and got 0.789g/cm³. I then plugged it into the equation for density and got

0.789g/cm³ = mass/10705mpg

The thing is none of this makes sense to me. I understand how to find the formula but how am I supposed to find distance only given the information? I would just convert miles per gallon to meters per gallon and then convert 100 grams to gallons, but how am I supposed to convert grams to gallons? Those are 2 totally different dimensions. I might just be thinking about this problem the wrong way, but right now I am not sure and any guidance would be greatly appreciated it. At first I didn't even understand why you needed specific gravity, but even using it to find the density is no use (I think) since I still get mass and not volume. Thanks in advance for any help.

 

[billy_joule]

0.789g/cm3 = mass/10705mpg

That equation has inconsistent units and doesn't match what you have in your relevant equations. Mpg is not a unit of volume.

You know that Density = mass/ volume
You have a density and a mass for the fuel so can find it's volume.
Using the units you have you'll get an answer in cc (cubic centimetres) which is equal to millilitres.

 

[Oannes]

That equation has inconsistent units and doesn't match what you have in your relevant equations. Mpg is not a unit of volume.

You know that Density = mass/ volume
You have a density and a mass for the fuel so can find it's volume.
Using the units you have you'll get an answer in cc (cubic centimetres) which is equal to millilitres.

Thanks for the heads up for some reason when my mind heard gallons I was so focused on volumes I wasnt even thinking about the rate of miles to it. Fixed that and then put into effect the information you gave me and it worked beautifully! Basically I just got my 126.74cm³ which was volume then converted that into liters then gallons. Ended up with approx. .0335 gallons which I then multiplied by miles per 1 gallon to get 358.62 miles. Then I just converted that into meters and got 577,483.89m. Thanks so much for the help this thing was racking my brain and now the culprit is apparent, I was too focused on the mpg as my volume when I needed the volume solved for the 100g.