You have two ropes. You know that each rope takes one hour to burn from one end to the other, but that the burning does not take place at a constant rate (i.e. half the rope may burn in one minute, and the other half will take 59 more minutes to burn).

How would you go about measuring a 45 minute time interval with just these two ropes?

Let us call the ropes as Rope A and Rope B. Then the conditions of the problem would be satisfied by the following steps:

1. Light both ends of Rope A simultaneously but light only ONE END of Rope B.

2. Wait till Rope A is consumed completely after 60/2 = 30 minutes. Now light the other end of Rope B.

3. The remainder of Rope B will now burn completely out in precisely 30/2 = 15 minutes.

Thus, we are able to measure out precisely 30+15 = 45 Minutes by means of the two ropes.