From TVTropes “Early Installment Weirdness” page for Star Wars:

When Vader is talking to Tarkin about Obi-Wan Kenobi being aboard the Death Star, Tarkin says “Surely he must be dead by now.” and Vader says “Don’t underestimate the Force”. This suggests that Obi-Wan is much older than his physical appearance would suggest and that a Jedi’s Force sensitivity allows them to live a lot longer than normal sentient beings. This is further backed up in the subsequent OT films which reveal that Yoda was 900 years old when he died in Return of the Jedi and Yoda says to Luke “When 900 years old you reach, look as good you will not” as if it was normal for human Jedi to live such a long lifespan. In The Phantom Menace, which takes place 32 years before A New Hope, Obi-Wan is shown to be a young man who’s still a Padawan learner and the EU established that Obi-Wan was only 57 years old in A New Hope, so this exchange between Vader and Tarkin now seems rather odd. Perhaps Tarkin’s reaction can be interpreted as him being surprised that Obi-Wan survived the Jedi Purge and remained hidden from the Empire for so long. As for Yoda’s age, it’s explained in the EU that members of his (unnamed) species live much longer than humans do and his comment to Luke was likely a joke.

I take it with a grain of salt but it’s an interesting mindset.

This could solve the whole discrepancy of the Empire only being around for 20 years because the Empire was created when Anakin became Vader, and Luke is only 20 years old, and yet everybody acts like the Empire’s been around for a long time and the Jedi are long extinct. Maybe Luke’s not actually that young. Luke and Leia are just able to retain their youth longer. Vader, the Emperor Obi-Wan, and Yoda have all been around way longer than the Prequels establish, which is why they all look older than their post-Prequel ages. It’s also why Owen and Beru look old: it’s actually been longer than 20 years.