### Brain Teasers

# Measure 45 Minutes

You have two ropes. Each takes exactly 60 minutes to burn. They are made of different material so even though they take the same amount of time to burn, they burn at separate rates. In addition, each rope burns inconsistently. How do you measure out exactly 45 minutes?

### Answer

Take one rope and burn it at both ends.At the same time, burn one end of the

other rope. When the first rope finishes

burning (ie. 30 minutes), light the other

end of the remaining rope (half of the

remaining 30 minutes gives you 15 minutes)

When it burns out, that`s 45 minutes.

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## Comments

Good puzzle. I got as far as the first part, burning both ends to get 30 min. I should have twigged how to get half of the half. Sometimes you don't see the obvious to light the second rope AT THE SAME TIME!

Easy when you know how!

??? But how can you be sure? Since It doesn't burn at a consistant rate???

otherwise a good teaser,

otherwise a good teaser,

That got me

ooops........missed this one

"You shouldn't play with fire!"

I don't like this one. It doesn't make any sense (to me)

if a rope burns at random speed, it could burn very, very, very slowly for 59 min, and then very fast for 1 min.

but this teaser had great potential

if a rope burns at random speed, it could burn very, very, very slowly for 59 min, and then very fast for 1 min.

but this teaser had great potential

andreja, It is implied that each rope takes sixty minutes to burn *if* it is burning from one end only.

But in the solution provided, the ropes are burned (at different times) from both ends.

So let's say the first rope has a "very, very, very slow" end which takes 59 minutes to burn a quarter of an inch. The remaining 13 inches (or whatever) will burn in 1 minute. Lighting both ends will therefore consume the "fast" section in a single minute, leaving 58 minutes of burn time for the remaing ~1/4 inch. Burning at both ends, this little stub will be gone in another 29 minutes.

Therefore, 30 minutes have passed, and the second rope has been burning the whole time, so it has 30 minutes of burn time left. Lighting the second end of that rope makes it burn twice as fast (another 15 minutes).

That help?

But in the solution provided, the ropes are burned (at different times) from both ends.

So let's say the first rope has a "very, very, very slow" end which takes 59 minutes to burn a quarter of an inch. The remaining 13 inches (or whatever) will burn in 1 minute. Lighting both ends will therefore consume the "fast" section in a single minute, leaving 58 minutes of burn time for the remaing ~1/4 inch. Burning at both ends, this little stub will be gone in another 29 minutes.

Therefore, 30 minutes have passed, and the second rope has been burning the whole time, so it has 30 minutes of burn time left. Lighting the second end of that rope makes it burn twice as fast (another 15 minutes).

That help?

blonde_genius and others are right: if the ropes burn inconsistently we cannot necessarily measure 45 minutes. JasonD isn't taking the word "inconsistently" seriously enough.

Inconsistent burning rate is irrelevant, so long as the total burn time is still 60 minutes. If you were measuring out the rope and burning half, then it would matter, but it doesn't in this puzzle.

It's like programming with concurrent threads. Or think of it like projects and man-hours.

Let's say you have 2 projects and they each take 60 man-minutes. If you put two people on the first job, it will be done in 30-minutes. If at the same time, you'd put a third person on the second project, that project would be half done when the first project finished, so it would only take 30 more man-minutes to complete. So if you add another person, that's only 15 minutes and it's done after a total of 45 minutes.

It's like programming with concurrent threads. Or think of it like projects and man-hours.

Let's say you have 2 projects and they each take 60 man-minutes. If you put two people on the first job, it will be done in 30-minutes. If at the same time, you'd put a third person on the second project, that project would be half done when the first project finished, so it would only take 30 more man-minutes to complete. So if you add another person, that's only 15 minutes and it's done after a total of 45 minutes.

cluemaster, think of it like this... 30 minutes after you light one end of the rope, the flame reaches a certain point on the rope, call it C. It's a 60 minute rope, so we know it would take a further 30 minutes to burn from C to the other end of the rope. But does it necessarily follow that it would take 30 minutes to burn from the other end of the rope to C? No, and there is the problem with the solution.

The rate must be consistently increasing with respect to the length (some function of length). it is missing from question otherwise it is not possible.

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