If your opponent cannot do anything active, then don't rush the position; instead you should let him sit there, suffer, and beg you for a draw.
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[Event "rated untimed match"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "Unknown"]
[Black "Unknown395"]
[Result "0-1"]
[Annotator "David Hayes"]
[BlackElo "0"]
[FEN "8/8/1p6/1P6/P1pk4/8/4K3/8 b - - 0 1"]
[SetUp "1"]
[TimeControl "0"]
[WhiteElo "0"]
1... Kc5 ( { Black can try: } 1... Kc3 2. a5 bxa5 3. b6 a4 4. b7 a3 5. b8=Q a2 6. Qb6 a1=Q 7. Qf6+ Kb3 8. Qxa1 c3 9. Qc1 c2 10. Kd2 Kb4 11. Qxc2 { White
wins with a large material advantage. } ) 2. Kd2 Kb4 3. Kc2 Kxa4 4. Kc3 Kxb5 { Black wins with a large material advantage. } 0-1