When a road authority constructs a drainage ditch to drain a highway over lands acquired for that purpose and the ditch crosses the right-of-way of any railroad, it shall be the duty of the railroad company upon demand of the road authority to forthwith carry the ditch under and across its right-of-way. The cost of carrying the ditch under or across the railroad shall be divided proportionately between the road authority and the railroad company on the basis of benefits accruing to each. Nothing in this section shall apply to or affect a county ditch, judicial ditch, or public drainage system.