Rope Clock: Solution
Let me assign some names to the ropes so as to identify them properly. Let one of the ropes be called as "Rope A" and the other as "Rope B".
I light up "Rope A" at both the ends, and I light up "Rope B" at one end only.
The ropes, I know, burn up completely in one hour. Since "Rope A" has been lighted at both ends, it will burn up in 30 minutes.
So, I have measured 30 minutes. Thirty minutes are over and in another 30 minutes, "Rope B" too should burn up. Immediately after "Rope A" has burnt up, I light the other end of "Rope B" also. Now, instead of taking 30 minutes to burn up, "Rope B" will completely burn up in 15 minutes. That is how I measure 45 minutes and that is how I keep my appointment!