Carol ruefully gives a recap in flashback as to how they came to be stranded in Cactus Creek ghost town. They took a detour from their trip to the Grand Canyon to set up in the ghost town. But a prospector, Zaccariah T. Brown locked them in the jail and stole their car because he thought they were stealing his gold claim. They managed to free themselves, but they were still stranded, without the car, food or water, so Mike and Peter went to seek help.
Carol rounds up the remaining kids to seek ways of raising help themselves. Greg manages to repair the old telephone, only to find Cindy on the other end. The town phones are connected to each other, not outside lines. Other attempts at setting up signals and finding water are equally fruitless.
Then the car returns, with Mike, Peter and Brown. Brown apologizes for his actions. He says he only meant to use their car to go into town and file his claim. He did intend to return, and he met up with Mike and Peter on the way. He gives them 10% of his claim (of which he has not any gold as yet) as compensation. All the Bradys see on the claim is an "X", but they forgive Brown.
The Bradys leave the ghost town and head for the Grand Canyon. The kids are awed when they see it. The Bradys go on a tour to savor the sights, including an Indian rain dance (and then a thunderstorm breaks out) before they make the mule trek into the Canyon the following morning. As the Bradys anticipated, Alice has problems with riding a mule, but she does manage the trek. They set up camp at the bottom for a three-day campout. Mike warns the kids against wandering as the environment is wild and can be dangerous. But Cindy and Bobby do wander when they see an Indian boy and chase after him. As a result, they get lost. Back in camp, Bobby and Cindy are missed and the family divide into search parties to look for them. But they have no success, and it is getting dark.