Help with Dimensional analysis?

Question

suppose your dorm room is 11.8wide by 12 ft long and 8.5 ft high and has an air conditioner that exhanges air at a rate of 1200 L/min. How long would it take the air conditioner to exhange the air. in your room once? (1 m cubed= 35.31 ft cubed)

Answer 1

This is unit conversions, not dimensional analysis.

Find Vft = 11.8 x 12 x 8.5
Divide Vft by 35.31 to get Vm3
Divide 1200 L/min by 1000 to get 1.2 m^3/min.
Divide Vm3 by 1.2 m^3/min to get exchange time.

Answer 2

0.284min
volume is 1203.6cft (cubic feet)

1203.6cft x (1m3/35.31cft) x (10000cc/1m3) x (1mL/1cc) x (1L/1000mL) x (1min/1200L) = 0.284min