Rook vs 3 pawns

Just played my approx'ly 24th OTB game ever.  Nip and tuck all the way toward the end.  Guy was from India, so not being able to pronounce his name, i called him Anand.  At one point i saw i could take his pawn, but i'd lose my N and so made a different move.  He said i just gave away the game and went on to beat me.  HAD i taken his pawn, giving up my N, i would have had 3 connected pawns with my King among them, against his K and Rook.  He said that 3 connected pawns with King amoung them wins every time agains K and R.   Is this true?  

Obviously not EVERY time. It depends on how advanced the pawns are, and the position of both kings.

Yes, okay, thanks FancyN.   Wish i'd taken notes of that game, but i believe my K was keeping his K at bay from getting close to my pawns, that is my K was in front of my pawns and he couldn't invade.  

Connected passed pawns are almost always worth a piece, and if you can make that happen (or have to sac to stop it happening to you) it's often worthwhile.   Naturally, closer to the end of the game it means more.   

I just had this happen and they resigned