If the boards are unable to agree and one of the boards appeals to the department, the department shall notify the auditors of the interested counties that it will, within ten days of the notice, at a named time and place within any of the interested counties, hold a hearing to determine all matters relating to any anticipated duty. At the hearing, the department shall fully investigate all questions pertaining to the disputed matters, and shall, as soon as practicable, certify its decision to the different boards. The department’s decision shall be final, and each of the boards shall immediately comply with the order in the same manner as though the work was located wholly within the county.