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Two uneven burning ropes

You have two ropes that each burn for exactly one hour when lit from one end, but they burn non-uniformly along their length.

Using only matches (no cutting to measure), how can you measure 45 minutes?

Outline:

  1. Light both ends of rope A and one end of rope B at the same time.
  2. When A burns out, 30 minutes have passed; then light the other end of B.
  3. B finishes in 15 more minutes. Total: 45 minutes from the start.

(One rope lit at both ends measures 30 minutes.)