You have two ropes. Each rope takes one hour to burn. These ropes are not identical, nor are they uniform; i.e. it does not necessarily take half an hour for half the rope to burn (if you have trouble visualizing this, imagine a rope of varying thickness across its length). With only these two ropes and a way to light them, how do you measure out 45 minutes?

“Burn one rope for 30 minutes and then light the second rope.”

This approach assumes that the ropes burn uniformly, which they do not. Since the ropes have varying thicknesses, burning one for a set time does not guarantee that it will burn exactly halfway.

“Light both ropes at the same time and wait until one is completely burnt.”

If both ropes are lit at the same time, there's no way to measure 45 minutes, as one rope may burn faster or slower than the other due to their non-uniformity, leading to an unpredictable total burn time.

“Light one end of both ropes and wait until one burns out, then light the other end.”

This method does not allow for accurate timing, as the burn rate of each rope is inconsistent. Without knowing how long it takes for one rope to burn completely, you cannot measure a specific time interval.