Jerome Gambit: Finish Him Off

The following position arose in the recent 1-minute Jerome Gambit game xjjettx-ViswanathanAdam04 at lichess.org. (I still can not wrap my head around the idea of playing the Jerome Gambit in bullet chess.)

It is White to make his 47th move. What is his quickest win? Remember, since it is a 60-second game, so if White has spent a second on each move played so far, he has only 14 seconds left to complete the game, so it is time to think fast.

If you saw 47.Rc8 (or 47.Rc7) followed by 48.Rh8 (or 48.Rh7) checkmate, good for you!

Instead, White played 47.Rf6, which allows the saving 47...R-any
freeing up the c-pawn to advance and Queen.

White was not the only player in time trouble, however, and after 47...Kh4 48.Rxg6 Black surrendered a pawn, allowing White hope to promote, as well.

That proved unnecessary, however, as after 48...Rf1 White checkmated, after all, with 49.Rh6.

So much of bullet chess is rapid assessment - and rapid moving - and in this case it was useful to visualize: 

Black un-blocking his c-pawn with a Rook move that checked White's King, gaining the needed tempo to promote (that is why White had moved his King to the protected square f4 just before we joined the game);

White's King and pawn hemming in Black's King, allowing for his Rook to achieve reaching the 8th rank followed by checkmating on the h-file; 

Later, Black un-blocking his c-pawn by moving his Rook anywhere (checking the enemy King was no longer necessary, as White's Rook had left the c-file); and

White realizing that the position had changed, and changed again, so that Black's King was again hemmed in, and checkmate was available.