Heavy piece endgame with 2 extra pawns-how to convert? 1r6/5pk1/2q1p1pp/3p4/r2P4/2P4P/PPQ2PP1/R3R1K1 w - - 0 1


It's White to move. 

White is 2 passed pawns up, but Black is very active. I'm sure objectively White is winning, but how? Black will attack and force me to move my a or b pawn, but the moment I move one pawn, Black will sink a rook next to it (a3 or b3) and paralyze my pieces.
1r6/5pk1/2q1p1pp/3p4/r2P4/2P4P/PPQ2PP1/R3R1K1 w - - 0 1

1. b3 Ra7 2. a4 Rab7 3. Reb1 Rc7 4. b4 Qxc3
5. Qxc3 Rxc3 6. b5 Rcc8 7. b6 Rb7 8. a5 Ra8
9. a6 Rbb8 10. b7 Ra7 11. Rb6 Kf6 12. Rab1 Ke7
13. Rc6 Kd7 14. Rbb6 Rxa6 15. Rxa6 Rxb7 16. Rcb6 Rc7
17. Ra8 Ke7 18. Rab8 Kf6 19. R6b7 Rxb7 20. Rxb7


You should move your pawns forward first since the a-pawn and b-pawn are passed. Do not allow black to blockade them. If pawns get blockaded, switch your attack to the kingside, and try to mate black king. You should move your queenside pawns forward quickly, and support them...if not, you might lose your chance.

Some very unpolished examples.

1r6/5pk1/2q1p1pp/3p4/r2P4/2P4P/PPQ2PP1/R3R1K1 w - - 0 1

1. b3 Ra3 2. c4 Rba8 3. c5 Rb8 4. Rec1 Qb7
5. c6 Qc7 6. Qc5 Ra5 7. Qc3 Ra3 8. Qg3 Qb6
9. Qe5+ Kh7 10. c7 Rc8 11. Rc5 Ra5 12. Rxa5 Qxa5
13. Rc1 Qxa2 14. Qf6 Qxb3 15. Qxf7+ Kh8 16. Qf6+ Kh7
17. Qe7+ Kh8 18. Qd8+ Rxd8 19. cxd8=Q+ Kg7 20. Rc7#


If rooks want to blockade, you may have to sacrifice pawns to promote and queen one pawn.

Do not forget your king safety. This variation is forcing, and promotes the pawns.

If you do not gain space on queenside, black can kill your pawns because of better mobility, so you must keep your edge and not fall from it.