The commissioners so appointed shall fix a time and place when they will hear the persons interested in the property to be taken, and in the benefits to be conferred by the proposed improvement, and shall give public notice of such time and place for at least ten days prior to the day of meeting in two or more of the newspapers published and circulating in the county. After having viewed the premises and heard the parties interested, they shall proceed to estimate and fix the value of the real estate taken and the damages caused by such taking, and ascertain and determine the amount of special or peculiar benefits conferred upon the owners of property benefited, in proportion as nearly as may be to the benefits which each owner shall be deemed to acquire, and to make report of their assessments to the court. They may report the damages awarded and the benefits assessed in any case in the same report or separately as they may determine.