Joe Hackett is the owner and chief pilot of Sandpiper Air, a small commuter airline that operates out of Nantucket Island. Joe and his family are Nantucket natives and Joe has a younger brother, Brian. Brian is an irresponsible wisecracker who's personality stands in stark contrast to Joe's fastidiousness.
In the recent past, Joe had been engaged to a woman named Carol, who'd left him at the altar for another man. The other man was Brian himself, who'd eloped with Carol. Joe hasn't spoken to Brian in six years. Brian's irresponsible nature has caused him to lose several potentially lucrative jobs -- Brian was also thrown out of an astronaut training program at NASA simply for inviting a woman on a date to the space shuttle training simulator.
Brian and Joe both entered adolescence without their mother, who'd left the family. Recently, the brothers' father had died and had been suffering from an unnamed mental illness and had left them both with very little. A short time after the funeral, Joe is contacted by a lawyer who sends Joe a package with a note saying it should only be opened in the presence of Brian.
Joe is reluctant to contact his brother because of the bad blood over Carol. Joe and Brian's childhood friend, Helen Chapel, who owns and runs the airport's lunch counter, presses Joe to call Brian about the note from their father. Helen seems to want to bridge the gulf between the two and reminds Joe that everything left behind by their father should be split with his brother, no matter the feelings between them. The counter attendant for Sandpiper Air, Faye Cochran, agrees with Helen. Joe finally agrees.
Brian shows up at the airport and wastes no time with his wisecracking attitude: he flies in on the terminal's other airline, Aeromass, a much larger and more successful company than Joe's, which is run by the opportunistic and sleazy Roy Biggins. Brian comments out loud about Roy's cost-cutting measures on his planes which compromise the safety of his passengers.
Joe meets Brian and the situation is immediately tense. Helen greets Brian; Brian later remarks that Helen has grown up into a beautiful woman (he's also attracted to her). In a private meeting, Brian tells Joe that a few months before their father died, he'd talked to him on the phone. Brian says that their dad said "You're rich." Joe and Brian open the package together; there is only a key to a safe deposit box on Nantucket. Believing that their father had left them a sizable amount of money, the two retrieve the box and find another key to a post office box in Boston. They take Joe's next flight there.
A few hours later, Joe and Brian fly back to Nantucket empty-handed. The postal box contained another key, which led them to several other banks and a locker at a bus depot where they found yet another key that had no location. Brian is flustered over the situation; he'd recently been fired from another job flying charter in the Caribbean. When he says he's broke, Joe chides Brian about stealing Carol. Joe also goes on to say that Carol was a sweet and kind woman who loved Joe dearly. Brian then tells Joe that Carol had left him for another woman shortly after marrying Brian. Joe is also taken back by the news that Carol had two-timed them both. Helen takes Joe aside and suggests that Joe hire Brian as a second pilot for Sandpiper. Joe refuses immediately, saying that Brian would be an unreliable employee. When he offers the job to Brian, his brother turns him down and plans to leave on the next Aeromass flight.
Faye suddenly says that the key they'd come back from Boston with likely fits one of the airport lockers in the mezzanine above the lunch counter. The brothers have Lowell Mather, the airport's mechanic and general maintenance man, open the locker. Inside is a small suitcase which he tosses down to the brothers. Joe and Brian both agree to split the contents in half and when the case is opened, dozens of spring snakes pop out, startling everyone. Also inside the suitcase is a picture of Brian and Joe as young kids in swimming suits. Written on the back is a final note from their dad saying "You're rich." The two realize that their father had planned the treasure hunt with the intention of having his sons spend time together and in the hopes of getting them to forgive each other. While they muse over the picture, making fun of each other, Brian asks Joe if his job offer still stands. Joe gives him the job.