Township and district roads for private and public use of the widths of 50 feet or less may be laid out from one or more dwellings or plantations to any public road, or from one public road to another, or from one or more lots of land to a public road or from one or more lots of land to a public waterway, on petition to the highway commissioner by any person directly interested. Upon receiving such petition, proceedings shall be had respecting the laying out of such road as in the case of other township and district roads. In case the highway commissioner or upon appeal, the county superintendent of highways, shall enter a preliminary order for the laying out of such road, such highway officer or officers making such preliminary order shall, if possible, and the parties are competent to contract, agree upon the total amount of damages, together with the portion thereof to be paid by the district, if any, as well as by each of the land owners benefited by such road. In case such damages cannot be determined or apportioned by agreement, the same shall be fixed as in the case of other township and district roads. The amount of such damages shall be paid by the person benefited thereby, to the extent and in proportion that they are benefited as determined and declared by the court. The remainder of the amount of damages, over and above that to be paid by the parties aforesaid, if any, shall be paid by the district as in other cases. The amount of damages to be paid by individuals shall be paid to the parties entitled thereto, before the road shall be opened for use. In all other respects the provisions of this Division of this Code relative to the opening, widening, alteration or vacation of other township and district roads shall be applicable also to the laying out, widening, alteration or vacation of roads for private and public use: Provided that the cost of the construction of the roadway, bridges and culverts and the maintenance thereof shall be borne by the parties paying for such road.