On our 110 day Alaska trip in 16 with 20 lb. propane tanks, we averaged about a month. 14k miles over that time, a few morning "warm ups" and showers when off the grid. Battery is a different thing. When off grid and all on battery, when the battery gets down to the mid 11 volt range most frig's will shut off to protect the circuit board. The newer RV trailers seem to have more "items" that draw off the battery when off grid like: back-lite radio, CO detector, GFI, usb ports...
My 2005 hybrid RV trailer I could get 3 nights off a battery with a shower every other night for 3 people. My 2013 hybrid trailer with a better group 29 single deep cycle battery I could only get 2 or 2.5 days. To supplement power I bought a 100 watt portable suitcase solar panel (Renogy) for when we are off grid or dry camping. Yes, it does the job. I can stay a week off grid as long as I get a little sun.
Our new 2018 ORV trailer I have two group 27 batteries and I "survived" a week dry camping last Sept in Acadia Nation Park in a very very very shady site. Ended the week at 11.95 volts. ( a fully charger battery is 12.6 volts)
#1, the basic battery is the group 24. Usually when you buy an RV from a dealer that is what they give you. The next size up is the group 27 with about 30% more power or storage capacity. Their usually $10 or $15 more at Walmart. I believe the group 29 is even larger. My new 2018 trailer I was only able to fit 2 group 27's between the front frame rails. They are about 2" longer than a group 24 basic battery...
#2 You will want to get yourself a plug in volt meter like the one pictured below (Amazon about $10) I live by this volt meter when off grid. Running the furnace is going to be the biggest eater of your battery. At least for us, running the pump for showers in the evening doesn't battery much. I might go from 12.55 volts to 12.50 for three showers.
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