Timing

[Blknight.aus]

inspired by a comment made in another thread about how long is a piece of string...

the objective is to time 15 minutes using 2 pieces of string that burn for one hour each... Heres the conditions..

you have only 2 wind proof matches, each match can only be struck once and will only stay lit for 10 seconds (perfect matches, they will strike on the first go, catch and stay lit)

you only have the 2 pieces of string.

the 2 pieces of string, other than the characteristic that they will both burn from one end to the other in exaclty one hour are in no other way similar. They do not burn in a linier rate, a given part of the string could burn for 10 seconds or 10 minutes and you have no way of knowing what part will burn for how long.

so given all of that,

how do you time 15 minutes?

[Outlaw]

with a stop watch :D

[95 Disco]

Cut them up to four pieces each, clever matches to light all eight pieces, and take and average ... or use a stop watch (as previously cited) or even a wrist watch .. close enough :)

[Ben]

Cut them up to four pieces each, clever matches to light all eight pieces, and take and average ... or use a stop watch (as previously cited) or even a wrist watch .. close enough :)

That was my initial thought too - cut them into quarters then take an average. For that, you need some way to measure burn times, and obviously you don't have anything to do so. Also, the second piece of string would be redundant.

We know burning a piece of string from one end burns for an hour, so burning it from both would halve it, regardless of its nonlinearity.

If we light string 1 at both ends and string 2 at one end, string 1 is burnt completely in half an hour. String 2 would still have 30 minutes left, so at that point we light its other end to halve the remaining burn time.

Our 15 minutes is from when string 2's other end is lit, until it's completely burnt.

[dobbo]

Why not make a circle out of the hour long rope?

Start burning and use the position of the burn to estimate the time fairly accurately, like a clock.

[Ben]

If it definately will take 1 hr to completely burn the string then how can the burn rate not be linear?

Coz it says right here:

the 2 pieces of string, other than the characteristic that they will both burn from one end to the other in exaclty one hour are in no other way similar. They do not burn in a linier rate, a given part of the string could burn for 10 seconds or 10 minutes and you have no way of knowing what part will burn for how long.

It's magic string.


The burning of the original string will ignite the 2nd (located at 1/4 length of original piece) at 15 minutes and the 3rd (located at the halfway point) at the half hour interval

Isn't this assuming a uniform burn rate? If the first quarter length burns in 10 seconds, then your 15 minute indicator would only be 14 minutes 50 seconds premature.

[dobbo]

Ben I realised my mistake and deleted the post.

However

I fail to see how a complete burn takes exactly one hour, yet cannot be linear


surely if the burn rate is accelerated then the complete burn time will be reduced.

Therefore the burn rate must be of a uniform acceleration to last exactly 1hr.

taking this to account


the burn can be uniform or controlled over a prescribed length.

for ease of brain at this hour in the morn prescribed length = 60cm

60cm = 1 hr to burn therefore 15cm = 15mins

[Ben]

C'mon man, it's 3:30 AM... in the morning... it's magic string ok. It just is.

:D

[dobbo]

Make a sundial out of rope 1.

Mark the position of the shadow

Use rope 2 as fuel (burns for exactly 1 hr in it's magic non linear way)

Mark the position of the shadow as 1hr after initial burn

Divide the angles by 4 and achieve 15 minute intervals.

[dobbo]

I presume splicing the rope would not effect the burn rate of this magic rope?

[Ben]

burns for exactly 1 hr in it's magic non linear way

The fact it's a non-uniform burn isn't magic. Perhaps the string has been coated in an accelerant, or perhaps not. Either way, it will be oscillatory combustion (oscillating burn rate and temperature - though in typical cases the differences would most likely be minute).

The magic is getting the string length correct to burn for exactly one hour.

But really, all this is irrelevant. We have all the information we need to solve the problem - one specified constant: the total burn time of both strings.

We need to find a quarter of the the total burn time, and we can get that by halving twice.

By burning the first string at both ends, we halve its burn time to 30 minutes. At the same time we started burning one end of the second string.

When the first string has completely burnt, we know we have 30 minutes left of burn time from the second string.

Igniting the other end of the second string, we halve that 30 minutes to 15 minutes.


On a similar note, I'm burning the candle at both ends... so I'm off to bed. Night!