rook and king vs king
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It's actually really easy to do IF you know how. Basically you use king opposition, check with the rook whcih forces the other K back, reestablish your K oppostion and check again. You repeat this until the enemy K is at the edge of the board, reestablish your K opposition and then mate with the rook. Obviously I'm no chess instructor 
so I got you a youtube link.
https://www.youtube.com/watch?v=WeMYBXEhCL0
thanks.