SOLUTION: Hi, I can't understand the answer as explained in the link below. http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.477023.html Ca

Algebra ->  Proportions -> SOLUTION: Hi, I can't understand the answer as explained in the link below. http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.477023.html Ca      Log On


   

Question 747824: Hi, I can't understand the answer as explained in the link below.
http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.477023.html

Can you kindly help me?
Thanks,
Moazzam
Found 4 solutions by lynnlo, MathTherapy, josgarithmetic, greenestamps:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by MathTherapy(10561) About Me  (Show Source):
Answer by josgarithmetic(39635) About Me  (Show Source):
You can put this solution on YOUR website!
Call the original unburned length for each candle, 1 unit.
Also note that rate*time is the amount of length burned.
                        rate           time           length remain 

first candle             1/5            x              1-(1/5)x

second candle            1/4            x              1-(1/4)x

"find the time, in hours, taken for the height of the first candle
to be four time that of the second candle ."

That should mean, 1-x%2F5=4%281-x%2F4%29.

To solve that,
1-x%2F5=4-x
5-x=20-5x
-x=15-5x
4x=15
x=15%2F4
x=3%263%2F4----------hours

Answer by greenestamps(13223) About Me  (Show Source):
You can put this solution on YOUR website!


Perhaps the solution is easier to understand if we work with the fraction of each candle that remains after a certain number of hours, instead of the length of each candle.

First candle:
burns completely in 5 hours
fraction of the candle that burns each hour: 1%2F5
fraction of the candle that burns in t hours: %281%2F5%29t
fraction of the candle that remains after t hours: 1-%281%2F5%29t

Second candle:
burns completely in 4 hours
fraction of the candle that burns each hour: 1%2F4
fraction of the candle that burns in t hours: %281%2F4%29t
fraction of the candle that remains after t hours: 1-%281%2F4%29t

Since the candles are the same length, the first candle is 4 times as long as the second when the fraction of the first candle that remains is 4 times the fraction of the second candle that remains:

1-%281%2F5%29t=4%281-%281%2F4%29t%29
1-%281%2F5%29t=4-t
%284%2F5%29t=3
t=15%2F4

ANSWER: the length of the first candle is 4 times the length of the second candle after 15/4 hours, or 3 3/4 hours, or 3 hours and 45 minutes.