How long can I run my A/C off batteries and solar?

How long can I run the A/C off my 200Ah LFP batteries and 400w solar?
Answer: 3 hours and 10 mins on a 92° day.
I set the thermostat to 72° with cool hi auto. This means that both the fan and compressor will cycle on and off at the same time to maintain the set temperature. I set the low voltage cutoff on the inverter to 12V (9%). I used 183Ah in that time and the solar provided 600w or 42Ah which ended up being about an extra 30 minutes.
I got 12 cycles in with the cycles getting longer as it got hotter. Anyway, good test for my system and I think I might could have made it over night on an 80° evening I had on my trip back in May.
Coleman Mach 3+ 13.5k BTU air conditioner
4 x 100w Renogy solar panels
2 x 100Ah Battleborn Lithium Iron Phosphate batteries
Xantrex Freedom XC 2000w inverter
Microair EasyStart 364 Bluetooth
I did all of the labor myself so the total cost of solar, batteries, inverter, easystart and supporting wires and components: $5700