Provides a common passageway for both food and air?

The correct answer is: pharynx.

The pharynx is a fibromuscular tube that conducts air from the nasal and oral cavities through the larynx into the trachea, and food from the oral cavity into the esophagus. It lies posterior to the nasal chambers, oral cavity, and larynx, and it communicates with the tympanic cavity of the middle ear through the auditory tube.