The strings are not clocks: they burn capriciously, without respecting proportions or halves. And yet, with just a lighter and some ingenuity, they can measure time precisely.

The two ropes

Reasoner
Timeless ingenuity

Riddle statement

You have two ropes and a lighter. Each rope takes exactly one hour to burn completely, but it does not burn evenly: one half can take much longer than the other.

How can you measure exactly 45 minutes?