Burning ropes puzzle

You have two ropes. Each takes exactly 60 minutes to burn. They are made of different material so even though they take the same amount of time to burn, they burn at separate rates. In addition, each rope burns inconsistently. How do you measure out exactly 45 minutes?

Answer:
 
1.) Take one rope and burn it at both ends. This will now take 30 minutes to burn.

At the same time, burn one end of the other rope.

After 30 minutes, the first rope has completed burning and the second rope has 30 minutes of burning left.

Now light the other end of the remaining rope, which will instead take 15 minutes to burn.

When it completes burning, that will be 45 minutes.

2.) We have two ropes A and B. Light A from both the ends and B from one end. When A is finished burning we know that 30 minutes have elapsed and B has 30 minutes remaining. Now, light the other end of B also so that remaining part of B will burn at double speed taking 15 minutes to burn. Thus, we have got 30+15 = 45 minutes.