The expenses and fees of sheriffs and other officers incurred in conveying convicted prisoners to any Department of Correctional Services adult facility shall be examined, adjusted, and approved by the county board and paid out of the treasury of the county in which the crime was committed. The county board shall allow expenses and fees at the following rates: (1) For the sheriff, six dollars per day for time actually necessary in conveying a prisoner to the facility and return; and (2) for each assistant or guard absolutely necessary, six dollars per day. No allowance for assistance shall be made when only one prisoner is conveyed to a facility. The county board shall allow the actual and necessary traveling expenses in going and coming. When the trip is made by automobile, mileage included in such expenses shall be computed at the rate provided in section 33-117 for county sheriffs and deputy county sheriffs for each mile actually and necessarily traveled by the most direct route.