# Two ropes and 45 mins [duplicate]

You have got two ropes of same mass, same material, same thickness and same length but mass is not uniformly distributed over the length. Both of the ropes burn in 1 hour but you cannot cut them in half and expect the two halves to burn in 30 minutes because of non-uniform distribution.

How would you measure 45 minutes using these two ropes?

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What is the probability that at any given instant (second), the sum of the length burnt by both ropes will be equal to the original length of either rope?

• @IAmInPLS I edited the question. Please look over it – prog_SAHIL Dec 7 '16 at 8:08

## 1 Answer

Fire up one on both ends and one at one end.

When the first one burns completely half an hour has passed, so you have half an hour remaining from the second one. Light the second on the other end. Now it burns on both ends and it will take 15 more minutes to finish.
Total 45 minutes

For the second part (I hope I understood the question properly):

Since everything burns in 45 minutes = 2700 seconds and if we consider the second the un-divisible unit of time, the sum of the burned lengths can be equal to the original length of each rope only in 1 second out of the 2700 and it's not equal for the rest of them. So the probability is $\frac{1}{2700} = 0.037 \%$ which is kind of slim.

• Correct answer for the first one. I just added the 2nd part, if u get it I will accept your answer. – prog_SAHIL Dec 7 '16 at 8:09
• I don't really understand the second part. – Marius Dec 7 '16 at 8:18