A lone pawn on the seventh draws against a queen when it is a bishop or rook pawn and the attacking king is far away, because the defender can offer stalemate in the corner.
This lesson belongs to queen endings, but every pawn-ending race ends here, so you must know the result before you start running. Many races finish with one side promoting while the other has a pawn on the seventh. If that pawn is a knight or centre pawn, the queen wins by forcing the king in front of its pawn and gaining time to bring the king up. If it is a bishop pawn (c- or f-file) or a rook pawn and the attacking king is far away, the position is a draw.