The mayor and city council in any city of the metropolitan class or city of the first class shall have power to license and regulate the keeping of toll bridges within or terminating within the city for the passage of persons and property over any river passing wholly or in part within or running by and adjoining the corporate limits of any such city, to fix and determine the rates of toll over any such bridge or over the part thereof within the city, and to authorize the owner or owners of any such bridge to charge and collect the rates of toll so fixed and determined from all persons passing over or using the same.