Upon the permission of the Mayor or Fire Chief, or pursuant to any agreement with a fire district for mutual aid protection, such fire equipment of the city as may be designated by the City Council as rural equipment may be used beyond the corporate limits to extinguish reported fires. The firefighters of the city shall be considered as acting in the performance and within the scope of their duties in fighting fire or saving property or life outside the corporate limits of the city when directed to do so by the City Council or the Fire Chief or some person authorized to act for the Chief and, in so doing, may take such fire equipment of the city as may be designated by the City Council.