When any road district desires to construct or repair any bridge or culvert as provided in Section 6-402, and has appropriated its share of the cost of constructing or repairing the same it shall be the duty of such other road district to make an appropriation for its proportionate share of the expense of such construction or repair. If such other road district fails or refuses to make such appropriation any court of competent jurisdiction, upon a proper petition for that purpose, shall issue an order to compel such other road district to make such appropriation; or the road district which has made its appropriation, may, after giving due notice to the other road district, proceed with the construction or repair of the bridge or culvert, and, if the construction or repair is reasonable in kind and cost, may recover from the other road district, by suit, such proportionate share of the expense as the other road district is liable for, with costs of the suit and interest from the time of the completion of the construction or repair. However, if the expense of the construction or repair of the bridge or culvert is unreasonable then the road district may recover only the other road district’s proportionate share of an amount equal to a reasonable expense for the construction or repair.