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You have two lengths of rope. If you set fire to the end of either of them, the rope will burn in exactly one hour. They are not the same length or width as each other. They also are not of uniform width (they might, for example, be wider in the middle than at the end), thus burning half of the rope is not necessarily going to take $30$ minutes. By burning the ropes, how do you measure exactly $45$ minutes worth of time?

Note : I don't know whether a solution even exists at all.

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HINT You can burn a rope at both ends.

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First burn the first rope from both ends and the second one from first end. After the first rope burns out light the other end of the second rope as well.It will give you 45 minutes.(I know I have told you Swapnanil, but this is for everyone else.)

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Light one rope at both ends, and the other rope at one end.

When the burn finishes on the first rope, 30 minutes have passed. Light the unburned end of the second rope.

When the second rope burn finishes, another 15 minutes have passed for a total of 45 minutes.

First phase: enter image description here

Second phase: enter image description here

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burn from the center and light the second rope immediately whenever the first side, burns completely, after that the time taken by the second rope to burn completely will give you the 45 min time

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