It shall be the duty of said trustee, upon the expiration of the time specified by him for the opening of such ditch, drain, or watercourse, and upon being satisfied by inspection and view that any section or sections of the same have not been completed, to sell such work by such sections to the lowest bidder by setting up written notices of such sale in at least three of the most public places in such township, specifying the time when such work shall be completed; said notices to be posted up for at least ten days before the day of sale; and said trustee shall take such bond or other security for the performance of such work, as he may deem proper; and such trustee shall make a fair and just estimate of the amount of costs made in all such proceedings, to be paid by each person interested in such proposed ditch, drain, or watercourse, and collect the same as hereinafter provided, and pay out the same in conformity with such estimates.