# Find Distance of Car, given Rest-Energy

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. 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!

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