A 12v car battery, connected to a 600watt 12v-240v inverter, powering a 400watt halogen heater, how long run?

I am trying to see how long a mains (240v) halogen heater will run for from a car battery (not connected to engine, standalone). i really wanna use an inverter connected to the car battery which will convert 12volts to 240volts to power the heater. the inverter is rated at 600watts, and the heater is 400watts, so how long will it run for before going flat? anyone help do the maths/theory for me?
Answer
You forgot to include the power loss created by the inverter.sorry jaktyee96