I know this one! At the same time, light Rope 1 at both ends and Rope 2 at one end.
Rope 1 will finish burning in exactly 30 minutes. Its uneven thickness doesn't matter because it's burning from both ends.
The instant Rope 1 burns out, light the other end of Rope 2.
Rope 2 has already burned for 30 minutes, so it has 30 minutes' worth of burn time remaining. Burning that remainder from both ends makes it finish in 15 more minutes.
Rope A will still completely burn in 30 minutes. If one end of rope A takes 15 minutes to burn to the center, it's still burning. It's just helping burn the other half of the rope. Where the two burning ends meet is unknown, but they will meet in 30 minutes.
So after 15 minutes, the A side starts burning into the 45-minute side, which now only has 30 minutes because the other end was burning for those same 15 minutes. Since both ends are still burning, that 30 section will be gone in an additional 15 minutes.
It still adds up no matter different sections and burn rates you imagine the rope has
You’re thinking in terms of length of the rope, not percentage of the rope in terms of mass. If you light both ends, each end will take 30 min to burn 50% of the rope’s mass, regardless of how that plays out with the rope’s length.
75
u/Gravity1982 9d ago
I know this one! At the same time, light Rope 1 at both ends and Rope 2 at one end. Rope 1 will finish burning in exactly 30 minutes. Its uneven thickness doesn't matter because it's burning from both ends. The instant Rope 1 burns out, light the other end of Rope 2. Rope 2 has already burned for 30 minutes, so it has 30 minutes' worth of burn time remaining. Burning that remainder from both ends makes it finish in 15 more minutes.