You have two ropes, each taking exactly 1 hour to burn completely — but each rope burns unevenly…

Why

Navya is correct that you cannot trust any POINT along a rope's length to mark a fixed amount of time, since uneven burning makes the halfway mark unreliable — but the puzzle does not need trusting a point on the rope, only trusting how long the WHOLE rope takes to finish burning, which is fixed at 1 hour no matter how unevenly it burns along the way. Light rope A at BOTH ends at the same time, and light rope B at just ONE end. Lighting both ends of A means two flames are eating into it from opposite directions — however unevenly, they always meet somewhere and finish burning the entire rope in exactly HALF the normal time: 30 minutes. The instant A finishes (at the 30-minute mark), light rope B's other end too — B now has 30 minutes' worth of unburned rope left (however that portion is shaped) and, being lit from both ends, finishes that remaining half in half the time it would normally take: 15 more minutes. 30+15=45. Test it: this works precisely because 'time to burn' only depends on how much rope is left, not on which particular part of the rope it is — uneven burning changes speed at any one point, but never changes the total time for a full, whole-rope burn. Her friend is right: lighting rope A at both ends and rope B at one end, then lighting B's second end exactly when A finishes, measures precisely 45 minutes.