Mathematics · Time and Work

A tank has three pipes: A, B and C. Pipes A and B can fill the tank in 5 hours and 6 hours, respectively, while pipe C can empty the entire tank in 12 hours. On a particular day, all three pipes are opened simultaneously at 10 a.m. Due to a mechanical schedule, pipe C automatically shuts off after exactly seventeen-thirtieths (17/30) of the tank is filled, which takes the first 2 hours of operation. After this point, pipe C remains closed and pipes A and B continue alone. At what time (to the nearest minute) will the tank be completely full?