38. Water jugs and burning ropes

You have two empty jugs and a tap of running water. One jug can hold exactly 3 litres of water while the other can hold exactly 5.

Using no other equipment, how do you get exactly 4 litres of water?

I heard this puzzle when I was a boy so it has been around for a long time.

The next puzzle however is of more recent vintage – I encountered it only in the heady days of the internet. It’s in the same genre as the water jugs puzzle but a little harder!

You have two ropes and a cigarette lighter. Each rope, when lit at one end, takes exactly one hour to burn to the other end, where the burning need not necessarily proceed at a uniform rate.

Using no other equipment, how do you measure exactly 45 minutes of time?