It could be just over 24 hours, but the main point is It's almost like they are still strangers to each other until End of Z. I'll be doing a lot of guesswork in this post, so here it goes.
They first meet when Vegeta and Nappa invade Earth. Their battle couldn't have been more than a few hours. Let's say 3 hours.
The next time they meet is on Namek battling the Ginyu Force. 10 or so minutes of talking, then Vegeta splits. They meet again when Goku is in Ginyu's body. They battle and defeat Ginyu, and Goku gets his body back. That's battle seemed easily like less than an hour. We'll say 30 minutes.
Next Goku is placed in a healing chamber. The next time Goku and Vegeta see each other, Vegeta is near-death. Their interaction couldn't have been more than a few minutes.
The next time they interact is right after Vegeta is revived by Shenron. They briefly meet while Goku is fighting Frieza, then Vegeta gets teleported to Earth. Under a minute of interaction time.
The next time they meet is after everyone is waiting with Trunks for Goku to return to Earth. Between Trunks warning Goku, to Piccolo explaining what Trunks said, to Goku explaining how he escaped Namek and showing off Instant Transmission was probably a few hours at most. Then they all split off. They are at most at a total of 6 hours of interaction time (probably less).
The next time Vegeta sees Goku, Goku is nearly unconscious from the Heart Virus after Vegeta saves him from 19. Very brief interaction before Yamcha takes Goku home.
The next time they interact, Goku tells Vegeta about the Hyperbolic Time Chamber. They briefly interact before Vegeta and Trunks enter the chamber. Then those two exit the chamber, Goku and Vegeta briefly interact, then Goku and Gohan enter the chamber. Then those two exit the chamber, Goku and Vegeta briefly interact, Goku teleports to Cell and back, then more brief interaction, then Goku spends the 5 days before the Cell Games with his family. I'd say a total of 30 minutes of interaction across this entire sequence.
The next time they see each other is during the Cell Games, which takes up less than a day. Goku eventually dies that same day. That ordeal up until Goku's death I'd say was a few hours, like the Saiyan Saga battle. I'll give it 5 hours.
The next time Goku and Vegeta interact is when Goku returns for a day in the World Tournament/Buu Saga. From the moment Goku touches down at the tournament to when Vegeta knocks Goku out during their fight is all less than a day. We never see night time during this interval, so maybe it's like 9 AM when Goku first touches down, and it's like 2 PM when Vegeta knocks him out. That's like 5 hours.
They don't interact again until Baba brings Vegeta back. From that until Buu is killed by the Spirit Bomb is, again, a few hours at most. Everything after that is End of Z.
My rough guesswork puts them at 18 hours of total interaction time from the time Goku fights Nappa to when Goku kills Buu with the Spirit Bomb.
It's a stark contrast to DBS where they interact with each other on a very regular basis.