Will King and Rook vs King and Rook end up in a draw if one player time ran out?

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Will King Rook vs King Rook end up in a draw by timeout insufficient material if one player time ran out? I was playing a rapid game earlier and my opponent tried to flag as he has more time than me (2 minutes: 10 seconds) in a rook vs rook-drawn endgame. It ended in a draw by repetition after 20 or more moves after a series of checks so it doesn't really bother me however I want to know whether it will end up in a draw or lost since I encountered a lot of situations like this before.

Strangemover

If there are rooks still on the board you will lose by timeout if you flag, regardless of the position being obviously drawn. The only time you will draw rather than lose if you run out of time is if the opponent has insufficient material to checkmate you eg.only a king, king and bishop, king and knight. These pieces cannot give checkmate alone, but a rook can.