Such drainage commissioners in any county of this State may jointly enter into contracts with the proper officers of such counties in any adjoining state to construct, repair or improve any such work of drainage, each to pay such proportion of the costs and expenses of the work as the contracting officials shall deem just. Such work of drainage shall be made on petition of landowners as provided for in this chapter in relation to other works of drainage and all other provisions of this chapter, so far as applicable, shall govern the drainage commissioners and other officers of this State in relation to such joint work of drainage; provided, such adjoining county or counties in other states shall pay their proper share of the necessary costs and expenses.