SOLUTION: Maria lights two candles of equal length at the same time. One candle takes 6 hours to burn out and the other takes 9 hours. How much time will pass until the slower burning candle

Click here to see ALL problems on Miscellaneous Word Problems

Question 640870: Maria lights two candles of equal length at the same time. One candle takes 6 hours to burn out and the other takes 9 hours. How much time will pass until the slower burning candle is exactly twice as long as the faster burning one? Explain your answer.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Since the candles can be any length, I will say
they are both units long, and the units
can be anything I choose.
The fast burning candle burns at a rate of units/hr
The slow burning candle burns at a rate of units/hr
Let = the units that the fast burning candle
burns off in hrs
is the length that is left
It is given that is the length left of the slow burning candle
is the length of the slow burning candle
that has burned away
-----------------
Equation for fast-burning candle:
(1)
Equation for slow-burning candle:
(2)
------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
In 4 and one half hours the slower burning
candle is twice as long as the faster burning candle
-------------
check:
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
OK