Light one of the ropes at each end so it burns toward the middle. At the same time light only one end of the other rope. Since the first rope is burning twice as fast as it would if only one end was burned it will take 30 minutes. When the 30 minutes are up the half rope remaining will have 30 minutes of burn time left. Now light the other end of the second rope so it is now burning at both ends. This will give another 15 minutes of burning. Total time = 45 minutes.