SOLUTION: There are 2 candles, one shorter than the other, which are lit at the same time. After a while the longer one is 12cm in height while the other one is 5cm shorter than it's beginn

Question 1068309: There are 2 candles, one shorter than the other, which are lit at the same time.
After a while the longer one is 12cm in height while the other one is 5cm shorter than it's beginning lenght.
You know that the shorter candle burns half as fast as the longer one.
What's their lenght on the exact moment when they're both equal in lenght?
Found 2 solutions by ankor@dixie-net.com, KMST:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
There are 2 candles, one shorter than the other, which are lit at the same time.
After a while the longer one is 12cm in height while the other one is 5cm shorter than it's beginning length.
You know that the shorter candle burns half as fast as the longer one.
What's their length on the exact moment when they're both equal in length?
:
let a = the original length of the longer candle
let b = the original length of the other candle
:
We know b candle is 5cm shorter and burns half of fast as a, therefore
While b burns 5 cm, then a burns 10 cm
:
a - 10 = b - 5
a = b - 5 + 10
a = b + 5
Given that a = 12 cm after burning away 10 cm
a - 10 = 12
a = 22 cm is the original length of the longer candle
:
replace a with 22 in the first equation
22 = b + 5
b = 22 - 5
b = 17 cm is the original length of the shorter candle
:
"What's their length on the exact moment when they're both equal in length?
22 - 10 = 17 - 5
12 cm when they are the same length

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Either a piece of information was lost somewhere along the way,
or this is a problem where you are supposed to say that there is not enough information.
There is no unique solution.
Maybe you have to write 2 equations with 3 variables and say that the system is "undetermined".

We know that after a while,
the originally shorter candle is 5cm shorter than its original height.
At that point, the originally longer candle, which burns twice as fast,
must be 10cm shorter than it originally was.
That means that the longer candle v was originally 22cm long.
It also means, that at 10cm per "while",
it will be completely burnt after 2.2 "whiles."
The shorter candle musty have originally been less than 22cm long.
We do not know the original height,
but the original height makes a difference.
If the original height is 11cm,
at 5cm per while, it would completely burn in 2.2 "whiles,"
just v like the longer candle,
so the answer would be 0cm,
meaning they would be equally long when they are both burnt up.
If the shorter candle starts with a length of 16 cm,
The 22cm-17cm=5cm difference will decrease (at 5cm per "while")
to 0cm in exactly 1 while,
and at that point both candles will be 12cm long.
If you pick another initial length for the shorter candle,
you get another result.
Maybe the shorter candle started with a 14cm length,
and after 1.6 while both candles are 6cm long.
Maybe the short candle was initially 21cm long,
and 0.2 while later both candles were 20 cm long.
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