In counties which contain ninety thousand inhabitants and less than one hundred and fifty thousand inhabitants the county highway engineer shall state in his order to the overseer the time within which the road shall be placed in good condition as required by section 61.240. The engineer shall cause the weeds and brush in the highways in his county to be cut once each year and he shall direct in writing to the overseer what roads and portions of roads shall be cut and state therein when they shall be cut. All weeds and brush shall be cut between the first day of June and the fifteenth day of July of each year.