Upon the filing of such petition it shall be the duty of the county board to set a day for hearing thereon, not more than fifty days from the date of such filing and to give notice by publication thereof for one week in some newspaper of general circulation in the county and the county clerk shall mail a copy of such notice to each of the landowners benefited by such ditch, as shown by the records of the office of the county treasurer, not less than ten days before such hearing.