Acarton measures 3 feet by 2 feet by 2 feet. a machine can fill the carton with packing material in 3 seconds. how long would it take to fill a carton that measures 4 feet by 5 feet by 6 feet?

1) we calculate the volume of the first carton:
volume=length x width x height
volume=3 ft * 2 ft * 2 ft=12 ft³

Therefore: 
A machine can fill 12 ft³ in 3 seconds.

2) we calculate the volume of the second carton. 
volume=length x width x heigth
volume=4 ft * 5 ft * 6 ft=120 ft³

3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.

12 ft³3 seconds
120 ft³      x

x=(120 ft³ * 3 seconds) / 12 ft³=30 seconds.

30 seconds.