@Sigil
You are mistaken about the solution being faulty. The second rope has been burning for 30 minutes, it does not mention ‘half a rope’ that is simply you misinterpreting the answer.

As it has been burning for 30 minutes means 30 minutes of rope is left, lighting the other side will reduce the time to 15 minutes regardless of the physical length that remains.

Your answer also borders on spoiler material, you should have flagged it as such.