216 cubic feet so plug in the numbers:

216 / 5 = 44 (I'm rounding everything up) = air exchanged every 5 minutes
44 * 1.5 = 66 = one 90 degree duct elbow
44 * 1.3 = 58 = resistance of carbon filter
+ 44 = 10 feet of duct
+ 5 = +/- 10% for error

Add it up: 44 + 66 +58 + 44 + 5 = 217 CFM

You could add two more elbows and still get away with 340 CFM or go with a 440 for good measure and room for growth. How big is your next room?