a rope burns in 60 minute.burning rate at a point is same as other side of centre.find minimum measurable time

Question

length of rope is not known. you are having only the rope, a matchbox and a pair of scissors.

Answer 1

This question could do with clearer expression. I'm going to assume the rope burns at irregular speeds but one half takes the same time to burn (half an hour) as the other half. And the question is, what's the shortest time you can measure accurately?
Answer is 1/4 hour. You align the two ends and cut the rope in half. Each half takes 1/2 hour to burn. Now you light one half at both ends. Thus you are burning the rope twice as fast, in 1/4 hour, the time it takes for the burning ends to reach each other. The two distances x1 & x2 and average burning rates v1 & v2 are probably unequal but we know the times are equal, i.e., t1 = t2 = t, and that the burning ends approach each other with velocity v1 + v2. We can show that the double-ended burn time t is half the single-ended burn time:
double-ended burn time t = (x1 + x2) / (v1 + v2)
single-ended burn time = x1/v1 + x2/v2 = t1 + t2 = 2t

Answer 2

hard subject. try searching with bing and yahoo. just that can assist!