A well-insulated, 80-gal (0.3028m³), electric hot-water heater initially contains water at 322 K (120 F). Hot water is withdrawn from the tank at 3 gal/min, while cold water at 283 K (50 F) enters to keep the tank full. The cold water mixes completely with the water in the tank at each instant. Because of a power outage, there is no energy input to heat the incoming cold water. Estimate the time required for the temperature of the outgoing water to reach 299.8 K (80 F). Assume constant water properties with ρ = 994 kg = m³ and c_p = c_v = 4149 J/kg · K.