100 amps (maximum reasonable deliverable power from a household connection without special considerations, assuming you want to do anything else at the same time) @ 240v = 24kw.

45 minutes = 18/kWh delivered over that amount of time.

200 miles on 18kWh? Bullshit.

Gasoline contains ~13kw/kg, and is approximately 6lbs/gal, or 2.73kg/gal. So a gallon of gasoline contains ~35kw of energy.

A gasoline engine is approximately 25% efficient, so of that 35kw about 9kw actually makes it to the wheels. Let's presume a nice, light car with decent (but not exemplary) aerodynamics and that this 9kw of energy can take us 35 miles.

Ok, so I can (assuming no losses) get 70 miles out of that "quick charge." Except there are losses. Charging a battery is (in bulk phase) about 80% efficient end-to-end (including the charger's losses.) The motor is probably roughly 80% efficient too. These stack, so now I get a net 45 miles out of that 45 minute "quick charge", or approximately one mile for every minute of charge time.

Meh.

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