Measuring 45 Minutes with Two Ropes

You have two ropes. Each rope takes exactly 60 minutes to burn from one end to the other, but neither burns at a uniform rate (a half-burned rope is not necessarily half-consumed in time). You may light either end of either rope at any moment. Using only these ropes and a way to light them, how do you measure exactly 45 minutes, and what is the shortest real time in which you can finish measuring it?