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Your average current draw for the TV and satellite will be approximately 10 amps. Your house batteries (2, 6 volt batteries in series) should be approximately 225 AH batteries. In theory you should get about 20 hours however several things come into effect and the amount of time will be slightly less. About 15 hours. However if you want your batteries to have a long life it is best to never discharge them more than 50% of their capacity. So 7.5 hours based on the above numbers. In any case never allow the voltage to drop below 10.5 volts. As mention in the above post your inverter should drop off line around 10.5 to help prevent you from damaging your batteries. If run any additional lights that will also decrease the time. These estimates are also based upon new batteries. If you much less time then estimated it may be time for new batteries.
In short, if your batteries are in good shape you should have no problems.
Have fun boondocking ~ Bill
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