Ethel is surprised by Lucy's understanding of Ricky and Fred's judging a beauty contest. Lucy claims it's "a new me". She changes her mind quickly when two buxom women in bathing suits appear at the door and ogle over Ricky and Fred. The old Lucy resurfaces instantly and comes up with a plan so the boys won't be judging any beauty contest.
The group is planned to take out a boat so Lucy and Ethel go to the boat early and tell the man to only fill the gas tank halfway. They plan to let the boat run out of gas and not until it's too late for the judging of the contest will the girls find the jug of gas that they have hidden onboard disguised as a jug of lemonade. The girls leave and the boys get to the boat. Ricky is giving Little Ricky and Fred a little nautical education when Little Ricky gets thirsty. Fred goes to find the jug of lemonade. He opens it and discovers it's gasoline. They wonder how someone could be so careless as to leave gas in a lemonade jug. Ricky takes the gasoline off the boat and leaves it on the pier.
The gang is enjoying their nice excursion on the water, except for Fred who's only concern is looking at his watch so they don't miss the beauty contest. Ricky finally decides it's time to go back so they won't be late. Before he can turn the boat around, the engine sputters and then dies. Attempts to restart the boat are futile so the boys decide to check out the Engine.
After time passes, the boys know that they won't make it back for the contest, it's too late. That is Lucy's signal to mention the fact that maybe they're out of gas and heard somewhere that they kept extra on the boat.
She goes right for the lemonade jug. Ricky points out that it's lemonade. Lucy let's it slip that it must be in the other jug which makes Ricky demand that she tell him how she knew there was another jug with gas in it. She's not sure whether to confess or jump overboard and swim to shore. She finally tells of her and Ethel's little plan. The boys are furious, not only have they missed the contest, but now they're adrift in the middle of the ocean.
Land is finally spotted and the group slowly washes ashore an island. They're not sure if it's inhabited or if they're stuck out there alone. They see a boat go by and try to wave it down, but the boat driver only waves back without stopping. Lucy also finds footprints of what she thinks are from a giant native. She follows them and they run right smack dab into Ethel.
The boys go off to look for anyone who might be on the island and the girls wait on the beach.
Ricky pokes his head through some bushes and sees what appears to be a giant native, just as Lucy had spoken of. Fred doesn't believe him but once he gets a gander at the native, he grabs Little Ricky and tries to run away. The native then speaks, he's not a native at all, he's actor Claude Akins. There's a whole movie crew on the island making a movie about the history of Florida and he's playing an early native. Ricky asks for gas and then asks for a big favor, he wants the actor's help in getting even with Lucy.
Back on the beach, Lucy and Ethel are having words because of Lucy's always getting her buddy into trouble. Lucy gets out a mirror to check out how horrible she must look and sees a giant native behind her. She tells Ethel but Ethel thinks it's just another of Lucy's wild stunts. Lucy convinces Ethel to turn around and when she does she screams. The girls jump up and start to run away. Lucy is captured and Ethel starts to run for help when the boys appear laughing.
The jig is up and the boys confess that the giant native is Claude Akins. The actor invites them all to big luau type party the movie crew is having. They're more than happy to take him up on his offer. From the bushes appear the two buxom beauties that were at the hotel and made Lucy and Ethel jealous. They are there as extras on the movie since the beauty contest was resceduled for the following day. Everyone goes off to enjoy a luau. Ethel gives Lucy a dirty look as they've gone through all of this trouble for nothing! Lucy tries to look sheepishly innocent.