Rook and pawns endgames

1.Rg1+ Kh7 2.Rg4 ( in order to prevent its king from checks by using Lucena rule.) Rd1 3. Kf7 Rf1+ 4.Ke6 Re1+ 5.Kf6 Rf1+ 6.Ke5! Re1+ 7. Re4 white wins.

This study is called Prokes manoeuvre. Two hanging pawns placed on the 3th (or 6 th) rank files and the files other than a and h files with the Kings and rooks create this position.
1.Kg4 e2
( or 1... d2 2.Kf3 Kg3 3.Ra1 e2 4.Ra3+ Kc2 5.Ra2+ Kc1 6.Ra1+ Kb2 7.Kxe2 draw )
2.Rc1+ Kd4 (2 ... Kb3 3.Kf3 d2 4.Rb1+ Kc2 5.Kxe2)
3.Kf3 d2 4.Rc4!+ Kd3 5.Rd4+ Kxd4 6.Kxe2 Kc3 7.Kd1 draw

No. 3

1.Kb7 Rb2+ 2.Ka7 Rc2 3.Rh5+ Ka4 4.Kb7 Rb2+ 5.Ka6 Rc2 6.Rh4+ Ka3 7.Kb6 Rb2+
( if not white can sacrifice the queen 8.Rxh2 Rxh2 9. c8 (Q) )
8.Ka5 ! Rc2 9. Rh3+ Ka2 10.Rxh2 !