Queen vs 2 connected passed pawns

White to move, how to continue?

My king is out of play and every time my king moves closer, his pawns inches even closer.  

What is the rule is this particular endgame? How far do the pawns have to march down in order for black to save for a draw? 

Stick your queen in front (like at h2) and you have more time than you may think to walk your king over.  The win should be pretty easy.

I don't know any rules for it, but the pawns have to be really far advanced to draw.  Like I said play it out just a few moves and you'll realize how hopelessly lost black is in the position you posted.  Basically they'd have to be far enough advanced that the queen can't just sit in front and make you lose 4-5 tempo while the king walks over to help.

So, basically something like this where the queen can't get in front at all.

That's just my idea of it.  I don't know if there are any special positions where black can draw with the pawns not so far up the board.

en.wikipedia.org/wiki/queen_versus_pawn_endgame

Black needs to get the f-pawn to the 7th rank to draw.  Nothing short of that will do.

In the initial position 1. Qb4+ wins immediately.  If Kf3 2. Qb7+ wins the f-pawn, Kg3, Kh3, or Kh5 is met with 2. Qe4 and the f-pawn again falls, and if Kf5 2. Qb1+ with 3. Qf1 to follow and black has no remaining counterplay.

A good example of a similar, drawn endgame can be found on this thread:

https://www.chess.com/forum/view/game-analysis/2-pawns-trump-a-queen

The side with the pawns can draw if they can get a rook pawn (a- or h-) or a bishop pawn (f- or c-) to the 7th rank (and even this loses if the attacking king is close enough), any single pawn loses on the 6th rank with the attacking side to play, unless the attacking queen is denied a key square by her own king (which is rare).

@Smallqpower11 is correct, this is a very important endgame to know.  Many endings come down to a pawn race, so it's essential to know how to win with the queen when you have it, and how to draw with the pawn(s) after the other player queens.  These scenarios come up fairly often.

...and i think most 3-pawns vs lone queen end up a draw !...(depending on white king...hasta avoid a checking coronation) 

Sort of very easy after 6 pints without even thinking.

get a rook pawn (a- or h-)...to the 7th rank

and a wonderful example of this is the game the other day in the S-cup in stl. sweircz vs so.

Looking back at my post #10, I think I can suggest a better approach in this position.

1. Go easy on the beer.

2. Think a little bit at least.

The tablebase gives the position as mate in 11 and I didn't even play accurately when it got down to mate with a queen.

Even so it still took me three attempts against SF14.

The salient point is you don't usually need to worry about the pawns creeping forward with backward pawns, because you can pick them off whenever. Sometimes, as above, an opponent's pawn creeping forward can be used to your advantage.

Turning to the question that was asked i.e., "How far do the pawns have to march down in order for black to save for a draw?", the strict answer, for general positions, is that, with White to play  at least one of the Black pawns must have moved at least one square from its starting position if Black is to draw.

This assumes the position is legal. So this is a legal draw

and would be a draw if the king and its attacking pawn were moved back a rank, but then all such positions are illegal.

If positions where both White pieces are attacked are ignored then I think the following applies:

White to play wins so long as neither pawn has reached its sixth rank, with the exception of either this (dead) position and its reflection.

or a limited number of positions with knight and bishops' pawns on the fifth rank, the White queen and Black king in the following position (or the reflection) and a remote White king.

This rule is the same whether or not the pawns are connected.

It cannot be extended forward because of positions such as this

If a pawn has reached the sixth rank this doesn't guarantee Black a draw e.g.

With the White king instead on a4 it would be a draw.  With the White king instead on c5 it would be a Black win.

With White to play Black can win only if one of his pawns has reached the seventh rank.

This applies irrespective of whether the pawns are connected except for a number of positions similar to the following with the White queen in different positions

(White queen on e.g. h4 White wins.)

not sure if ur 4th diagram izza draw. yes if lone b-pawn on f2 and king can reach h1.

No, you're right, it wasn't. I've removed it.

Mind you confused by the reference to f2. Did you mean c2 or were we talking about different diagrams? I've now lettered them for ease of communication.

uhhh...diagram D. and if the boards lower left is square a1, then yes f2.

still not certain if white hazza win. i see:

1. Qb3  Kf2

2. Qc2+ and the queen walks in to try to control e3 and eventually occupy it. not convinced it can tho.   yee !!

OK we were talking about different diagrams.

In D after 1.Qb3 f2 you would have a well known KQKP draw in the absence of the e4 pawn, so Black can let White have that pawn. Pushing it, if necessary, will convince White it's a good idea to take it.

Here it is against SF14, both as SF would play it and with your suggested 1.Qb3.

But after 1...Kf2 Black is rubber ducked either way (with some difficulty for White).

C is the same idea but with the bishop's pawn one square further back

and you can set up similar draws with the pawns behind the seventh rank based on the rook's pawn draw in KQKP

in diag 2 why would a/o ever play 3....c2 ?? just play 3...b3. dont gettit.

3...c2 was to illustrate the point about the KQKP draw, i.e. Black doesn't mind if White takes the knight's pawn after his bishop's pawn reaches the 7th. rank;  3...b3 is just as good, but Black can't get both pawns home, so it's a draw either way e.g.

(But in the first diagram only 1...f2 will do.)

That ignores the position of the white king which, out of laziness, I put as far away as possible in the original diagram. With the other pieces in their positions after White's move 3, Black loses with 3...b3 for about twice as many placements of the white king as he does with 3...c2, so 3...c2 really shouldn't look so unusual. 

E.g here ...b3 loses for Black, but ...c2 still draws

There are no placements of the white king for which the reverse is true.

Rule of thumb: The simplest way to win any queen-vs-pawns race is by getting the queen in front of the pawns.

In the initial position, I would instantly play 1. Qh2 f5 2. Qg2. This effectively stops the pawns, giving white all the time needed to bring the king into play.

Dsmith42's 1. Qb4 works just as well. I just like getting the queen in front of the pawns, then the rest of the moves play themselves.

@Bramblyspam

Well that will win, but then almost anything will. The original position is a mate in 11. How would you complete the mate in 11 from there? Notice that I manage the mate in 11 against SF14 in #12 without ever putting the queen further down the board than the leading pawn, as opposed to my (dismal) attempt in #10 where I did. 

And the rule of thumb should be taken with caution. It wouldn't be advisable in positions like E in #12, nor, less flippantly, after ...b3 in the second position in #18, where I think it's necessary to work from the back of the pawns.

E.g. this loses White a half point