how long does it take to fill up a $3$ gallon tank of air with an air compressor? there are two flow rates provided that show us how fast the compressor pumps air into the tank while the tank is gaining pressure. these two flow rates are $6\mathrm{.}3$ scfm when the tank is at $40$ PSI and $5\mathrm{.}1$ scfm when the tank is at $90$ psi. the flow rate will constantly change as the tank gains pressure up to a stopping point at $200$ psi. please solve taking into account the changing of the flow rates as the tank fills with air. please do not just find the flow rate at $200$ PSI and use that.