There are two lengths of rope.
Each one can burn in exactly one hour.
They are not necessarily of the same length or width as each other.
They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.
By burning the ropes, how do you measure exactly 45 minutes worth of time?
If you know the answer, keep it to yourself until 3.30
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Light both ends of one rope. That will burn down in 30 mins. At exactly same time light one end of the other rope. When the first rope has completely burnt, the second rope will have half an hour left to burn. At this point light the other end of the second rope, then it'll burn away in 15mins. Once both ropes are completely burnt 45 mins will have elapsed.