I remember drawing a rook and two pawns vs. rook position with g- and h- pawns. I was the losing side. Basically, 1) prevent king mobility, 2) win the rook pawn and 3) play the first rank defense on the g-pawn.
In rook endings, there are many positions where two pawns are not enough to win. Only opposite-coloured bishop endings present a higher drawish trend.
Excerpt From: "100 Endgames You Must Know: Vital Lessons for Every Chess Player Improved and Expanded" by Jesus de la Villa.
But what if the opponent plays accurately, and doesn't drop pawns?
The idea is as follows: set a blockade on the seventh rank by playing Rb7 and Kh7. If the king approaches, check him with your king on g6. If the rook attacks your king on h8, White has no time to move his King forward on the next move because of ...Kxg8.
To win, prevent the opponent from enacting this blockading strategy. Judging by the original poster's position, Black plays 1...Ra5 (or 1.Ra1 Rb5) and blockades.
EDIT It is a draw only if the pawns are pushed without thought as another poster suggested. The strategy is to push slowly, one at a time and to avoid drawing positions as listed.
A two pawn advantage in most cases guarantees the win. But there are quite a few drawn positions, particularly when one of the pawns is a RP (as in OP).
Excerpt from Rook Endings. Smyslov and Levenfish.
This book is a great reference on such positions. There are eight pages devoted to it. Here is an excerpt: