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I really do think that you're missing an important detail of your puzzle. As it is, I really don't think there's enough information to solve it.
However, here's a puzzle for you!
Show that, if the rope burns symmetrically (burns at the same rate in either direction), then lighting both ends of the rope at the same time (like tying the two ends together, for example) will result in the two burns meeting up with each other in 30 seconds, regardless of the rate in which the rope burns!
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