Problem - 4662
$\textbf{Burning Ropes}$
Two ropes have different densities at different points, but both take exactly an hour to burn. Is it possible to use these two ropes to measure $45$ minutes? If so, how? If not, please explain.
$\textbf{Solution}$
Yes, it is possible. Light both ends of the first rope and one end of the second rope. It will take $30$ minutes for the first rope to burn out. At that time we light the other end of the second rope. Because at this point, the second rope has already burned $30$-minute, it will take another $15$ minutes to burn the rest. Hence, when the second rope burns out, it is $45$ minutes in total.