32.3 hours
Reasonable load range: 12.9 hours to 80.8 hours
Calculation
3,800Wh × 85% usable efficiency ÷ (100W × 100% duty cycle) = 32.30 hours.
What can change the result
Actual device wattage, battery age, ambient temperature, inverter standby draw, conversion losses, power-factor behavior and cycling frequency can all reduce or extend runtime.
Check output before connecting
The battery or UPS needs at least 250W continuous capability and about 400W surge capability. Watt-hours alone do not prove compatibility.