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Please help me in these 2 Rook Endgames

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I recently faced a few confusing rook endgames in my blitz games.
 
This first one I thought I was winning the whole time being up 2 pawns but in the game review it was shown drawn till a particular move (62nd) my opponent made. Please suggest what I could have done differently and how my opponent could have held a draw being down 2 pawns. Things are not clear from the engine..
In this one I had now idea when to stop trying to win. I just kept blitzing moves till I lost. Can someone tell me if I could have forced a draw at some point? I think I should have kept my rook on the 8th rank once black pushed his pawn to the second rank and fixed his rook and keep checking the black king from the back if it tries to come help. Or should I have done something else?
enri55

Please traducción al español