We have the same trailer and Fridge. It will stay running and keep a steady cold (-2F for freezer) for at least 5 hours when hooked to the inverter. We also only have one battery and since we always stay where there is shore power, that is all we have needed in over 12 months of travel on the road. Be aware that the fuse on the inverter tends to pop every time you hook up or disconnect shore power. I just push the button and make sure the voltage is showing right before shutting the bay and pulling out. I have never tried driving over 5 hours in the heat so not sure if the battery will go dead or not. I do have dual alternaters to generate added power though.
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Ray, Cindy and Goldie the Lab
2018 Montana 3791RD
2017 RAM HD3500, DRW, Cummins Diesel
Jacksonville, FL
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