Allow me to present, a rather possibly crazy theory.
Paradise Falls is the Fountain of Youth.
To consider evidence, we shall bring in a lot of plot elements from the movie.
First of all is Muntz. This man seems to be at least 50 years old during the film being shown to the young Carl. Shown heading for the Falls all that time ago, supposedly never to be heard from again. However, when we see him again later on in the movie, it appears that he has aged possibly 10 years at the most. Let us assume that is how long it took for him to actually find Paradise Falls, and the rest of the time, establishing his hold on the island, looking for the Snipe.
Enter Carl ~50 years later. He is depressed, cranky, old, and weak. Upon reaching the Island of Paradise Falls, he seems fully revitalized. Not requiring his cane, able to move and pull the house over a long distance, as well as running and keeping up with Russell rather well, seemingly surpassing his endurance easily.
And then we have the dogs. It is no secret that dogs have a much shorter lifespan than humans. But in order for Muntz to have as many dogs as he does, one can assume that because the Island has Fountain of Youth properties, it is possible the dogs are affected as well, preserving their life during the long stay before Carl arrives.
Yes the theory does seem crazy, but it offers an interesting take on the movie, if they somehow traveled to the same, or similar, Island as Lost, which was shown to have healing/slow aging properties.