The rule of thumb for 120 volts to 12 volt amps is divide by 10. So 340 watts will draw about 34 amps at 12 volts (yes I know this is not the "proper" way to do it but it takes into account several thins like inverter effiency and wire loss.. it works out amazingly close).
So with 440 amp hours 220 usable you habe 220/34 hours of run time or about 6 hours. at 50% you MIGHT make it 12 hours but it will be tight.
NOTE this does not count the starting load.. So I doubt you will do 12 hours plus not all inverters will let you run 'em down to half full (THey tend to be set for MARINE/deep cycle which should be kept 3/4 full or better).