If the county board of any such county, after reasonable notice in writing from such other county board, neglects or refuses to construct or repair any such bridge or culvert when any contract or agreement covering the division of cost has been made in regard to the same, the county board so giving notice may construct or repair the same and recover, by suit, such amount as shall have been agreed upon of the expense of so constructing or repairing such bridge or culvert, with costs of suit and interest from the time of the completion thereof, from the county board so neglecting or refusing.