You are going to pressurize a tube using a mechanical pump. The standard bicycle tube is wrapped around a 24-in. diameter metal rim. The inflow to the pump is constant at 1 ft³/min. The density of the air leaving the pump is 0.075 lb_m/ft³. The final inflated volume of a bicycle tube is 0.6 ft³. The density of air in the inflated tube is 0.4 lb_m/ft³. The atmospheric pressure surrounding the system is 14.7 lb_f/in². Assuming that there are no leaks anywhere in the system, please calculate the time necessary to pressurize the tube if there initially is no air in the tube.