Candles Burning
We have two candles of different sizes. The lengths and the thicknesses are different. The longer candle has a 3 1/2 hour burn time. The shorter candle has a 5 hour burn time. They are lit at the same time and burn for two hours. After the two hour burn, the candles are the same length.
What fractional part of the longer candles original length, is the shorter candles original length?
What fractional part of the longer candles original length, is the shorter candles original length?
posted by Zaux at
8:27 PM
12 Comments:
I know the answer, but I refuse to answer since "lighted" isn't a real word. That's my excuse and I'm sticking to it.
I think it might be 5/7.
"Lighted" is a real word, but "lit" should have been used. After the candles were lit, they were lighted. I know it sounds wrong, but it is right.
Longer candle: original/final length = 3.5/(3.5-2) = 7/3.
Shorter candle: original/final length = 5/(5-2) = 5/3.
As the final lengths are the same for both, the ratio of the shorter original length to the longer original is (5/3)/(7/3) = 5/7.
so sorry ...for the purists, it will be changed to lit
5/7 it is
I came up with 0.714, mainly because I don't understand fractions.
On the use of the word "lighted" - this was the correct term until around WW1 when we Brits became a little americanized.
I speak from experience you young whippersnappers, you!!
5/7 = 0.714285714285714285...
I agree, "lighted" is archaic. I'm a 57 (not 5/7 ths) year old whippersnapper.
Googling with "trade currency euros dollars" quickly led me to: http://www.oanda.com/currency/converter/. I expect there will be many such sites.
Assume rate of burn/volume is constant (volume can be expressed in hours worth of burn)
then
A = cross sectional area L=length
A1*L1=5
A2*L2=3.5
After 2 h a volume V burns
V1=A1*L1-V=5-2=3
V2=A2*L2-V=3.5-2=1.5
After 2h
L1=3/A1
L2=1.5/A2
and L1=L2
1.5/A2=3/A1
A1=2*A2
sun into A1*L1=5
2*A2*L1=5
A2=2.5/L1
sub into A2*L2=3.5
2.5/L1*L2=3.5
L2/L1=3.5/2.5=7/5
or L1/L2=5/7
Answer:
shorter candle is 5/7 length of longer candle
Cam
This post has been removed by the author.
Oooooh, Cam! If the candles were made from a different quality wax, your areas would be wrong. The longer candle could also have been fatter as well.
Luckily (snigger), you got the right (that's left for Ragknot) answer ;).
- Mr. Pedantic.
The question is impossible to answer as insufficient data has been given. You don't say whether or not the candles burn at a uniform length per unit time.
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