Find Distance of Car, given Rest-Energy

[blue_lilly]

Homework Statement

Suppose one gallon of gasoline produces 1.01×108 J of energy, and this energy is sufficient to operate a car for 18.2 miles. An aspirin tablet has a mass of 332 mg. If the aspirin could be converted completely into thermal energy, how many miles could the car go on a single tablet?

Homework Equations

The Attempt at a Solution

1 gallon of gas= (1.01E8) J
Distance of car(on gas)= 18.2 miles
Mass(aspirin)= 332 mg
Looking for
Distance of car(on asprin)=?

I converted the mass from grams to kilograms.
332mg = (332E-3)g = (332E-6)kg

*After this I'm not sure if I'm doing the right thing.*
The problem says "converted completely into thermal energy" so I'm assuming that this means I need to find the rest energy.
Erest=mc^2 [m=mass in kg; c=speed of light=(3E8)m/s]

=(332E-6)(3E8)^2
=(332E-6)(9E16)
=(2.988E13) J​

I then set up the energy of gas, distance on gas and the energy I found abvoe of the asprin, to solve for distance on asprin?

(distance of gas)/(energy of gas)=(distance of aspirin)/(energy of aspirin)
=(18.2 miles)/((1.01E8)J)=(?distace of asprin?)/((2.988E13)J)
=[(18.2)(2.988E13)]/(1.01E8)
=(5.43816E14)/(1.01E8)
=5384316.832 miles = (5.38E6) miles​

However that answer is incorrect and I'm not sure if I am even using the right formulas for this problem.

Any help would be greatly appreciated!

 

[Patolord]

is the answer 0.001242742 miles?
im not a guru btw

 

[blue_lilly]

The correct answer is (5.38E6)mi. My calculations were correct, I just had my units of measurement wrong.

 

[NascentOxygen]

Hi blue_lilly. I'm pleased that the physics forums was able to help you to solve your problem on this occasion.

 

[Patolord]

errr so a gallon of gas get you 18 miles and an aspirin 5.38*10^6 miles ?

i guess we been using the wrong fuel all this time...

 

[blue_lilly]

errr so a gallon of gas get you 18 miles and an aspirin 5.38*10^6 miles ?

i guess we been using the wrong fuel all this time...

If only it really worked like that, we would saving a lot of money. C: