Burning 2 ends of it at the same time llets you measure 30 minutes. How can we ensure the above statement because according to question “the first half might burn in the first 10 minutes and the second in the remaining 50”
Non-homogeneity will not matter. Assume the length to be x, so If you burn 2 ends at the same time it doesn’t matter if it burns completely at point x/2, x/3, or x/4. We are just measuring the time so when it burns completely we’ll know that its 30 min.
Let suppose rope is of length ‘x’, and in 30 min t length is burnt if lit from , say, end A. Hence if the rope is lit from other end, say, B x-t length will burn in 30 min, given complete rope burns in 1 hour. If rope is lit from both end, after 30 min one end will cover t length and other x-t length so overall x distance is covered.
- burn 2 ropes in opposite ends
- when the fire in both ropes meet, 30min has been over
- at this moment lit another end of one of the rope, it takes 15min to burn the remaining part
so 30 /15/ 30+15 min can be measures