For the purpose of draining the right-of-way of any highway, the Department may make agreements with any ditch company or corporation with respect to the cleaning of ditches, or widening, deepening or extending ditches. For this purpose the Department may pay a fair and proportionable part of the expense thereof, the expense to be mutually agreed upon before the work is undertaken; and provided that the ditch company or corporation shall levy taxes sufficient to pay its fair and proportionable part of the expense, and provided that the work of cleaning, widening, deepening and extending the ditches shall be under the supervision of the Department.