Hi there,
Hopefully this isn't too simple for everyone I found it interesting and if so I'll try harder next time! I've known about pawns on the sixth beating a rook and I've used it a fair amount to win games. I found the following position (with white to move) interesting as it adds to this idea and hopefully you can use to win some games. I love rook endgames in general so when I see something surprising in them it sticks. The only problem with this position is there are a couple of good moves in the starting position. Though to be fair the most obvious one is difficult to win and the author gives the line as shown in the solution below.
Looks a little drawish based on the position of the rook but there is an advantage and it is black who is fighting for the draw here. There is a move however that removes all doubt pretty immediately. Take a look and see if you can find it. Solution and details below.
This comes from secrets of grandmaster chess -Nunn 1997 and the game is Nunn-Pitt 1970.