I've searched the forum and not found this puzzle here before, apologies if I've missed it.
The Puzzle:
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?
Ok at t=0, light one rope at both ends and the other one at one end
The first rope will burn out in exactly 30 mins, at which time you light the other end of the other rope. The remainder of this rope will burn out in a further 15 mins.