The shower uses up to 5 gallons of water per minute. It takes 440 Btu to heat one gallon of water, or 2200 Btu per minute. Thus, a 10 minute shower uses 50 gallons of water and 22,000 Btu of energy.
Each gallon of gasoline is equivalent to 125,000 Btu. At 30 miles per gallon, i.e. 0.033 gallons per mile, my 4 mile journey to work (which takes about 1/2 hr in berlin) gives me 0.133 gallons which is 16667 Btu. Is that right?