Whenever railroad tracks cross a public highway at grade, outside of incorporated cities and villages, the owner of the railroad tracks and the county board of the county in which such crossing is located may agree upon any change, alteration, or construction of any crossing as will promote the public convenience or safety, and they may also agree upon the relocation of any highway so as to eliminate such crossings entirely or so as to carry them over or under such railroad and upon the apportionment of the expenses incident to any such change, alteration, relocation, or construction between the owner of the railroad tracks and the county or other public authority in interest.