Can I win as black here? In the below position, I'm playing as Black and it's my turn. 

[FEN "8/8/1K6/2P5/1P6/8/8/6kq b - - 0 1"]


I've recently gotten back into chess, and this one is driving me crazy. I can't seem to figure a way to win, only draw.  I don't appear to be able to get my king close enough. Can I win as Black? Any ideas would be great!
Yes, it is really an easy win.

The first move is 1...Qe4; 2.Kg4 Kc7, and note that white cannot make any progress without losing one of the pawns, leaving an easy win since your Q can get to g8 after winning the first pawn.

[FEN "qk6/8/8/6P1/5P2/6K1/8/8 b - - 0 1"]

1... Qe4 2. Kg4 Kc7


This is with it going the other way. It is harder, no question, but the first thing is to get the queen in front of the pawns.

 [FEN "8/8/1K6/2P5/1P6/8/8/6kq b - - 0 0"]

 1... Qa8 2. c6 Qb8+ 3. Kc5 Kf2 4. b5 Ke3 5. b6 Qe5+ 6. Kc4 Qa5 7. c7 Qa6+ 8. Kd5 Qb7+ 9. Kd6 Kd4 10. Kd7 Kc5 11. Kd8 Qxb6