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30 seconds: light both ends of one rope simultaneously -- because it is lit twice and the burns don't meet until the rope is gone, the rope disappears twice as fast. I don't think any additional information is necessary for this answer to work.
are the ropes identical?
EDIT: if they are identical, you can use the saltfish method, and when the burns line up (ie. after 30 sec), you can light the non-burning end of one of the remaining pieces. It will burn up 15 sec. later.
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