[Larry Lucido]

Burn one rope at both ends, and light the second rope at one end. The first rope will burn through in a half hour and the second rope will burn halfway through. Light the remaining second rope at both ends and it will take 15 minutes to burn through.

Or just look at your watch or your phone.

[Enterprise]

Throw both ropes on the barbie.

[ifinnegan]

All right. This is crap. For one thing, you have to pay for the answer.

I see Larry posted the answer.

But it’s not an answer to the question as asked and illustrated, nor is it right in terms of the question as the answer purports it to have been asked. The illustration and wording indicates the rope is being lit at the side, not the end, and burning through the rope.

Here’s their answer without the solution.
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“Because the ropes burn at inconsistent rates, you can’t simply measure 75 percent of the way down one rope and call that 45 minutes. The rope might burn slightly faster or slower in that last 25 percent. However, if you light one of the ropes on fire at both ends at the same time, it will burn up in 30 minutes, even if one side burns faster than the other.

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Larry’s answer makes sense after ignoring a mistake “ the second rope will burn halfway through”. The question explicitly said the rate of burning does not correspond to length of rope burn, ie the rate varies. The time will be halfway through but the rope could be any percentage burned up.

[ProtectOurFreedom]

“Burn one rope at both ends, and light the second rope at one end. The first rope will burn through in a half hour and the second rope will burn halfway through.”

Rope 1 — Yes, regardless of local burn rates, the rope will burn through in 30 minutes.

Rope 2 — No. The second rope could burn through 90% in that 30 minutes. Or it could burn through 10% in that 30 minutes. So you have no way of knowing if Rope #2 will burn halfway through.

[HandyDandy]

”Burn one rope at both ends, and light the second rope at one end. The first rope will burn through in a half hour and the second rope will burn halfway through it’s total allotted time of one hour. Leaving 30 minutes .The second rope therefore has half of its allotted time left (30 minutes). By starting it burning from its other end, it will be totally consumed in 15 minutes. Bringing the total passage of time to 45 minutes.

FIFY

The only main difference is that you stated “the second rope will burn halfway through.” That left it unclear whether you meant halfway through by length or by time. Of course, you meant by time.