To reupholster a piece of antique furniture, Analemma Antiques charges a flat fee of $300 per piece, plus a labor cost that is directly proportional to the square root of the number of minutes it takes to complete the piece. Recently, Analemma Antiques charged a total of $700 for a piece of furniture that took 10 hours and 25 minutes to complete. What is the charge, in total, for a piece that takes 6 hours and 40 minutes to complete?