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

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Question 145749: Maria lights two candles of equal length at the same time. One candle takes six hours to burn out and the other takes nine. How much time will pass until the slower-burning candle is exactly twice as long as the faster-burning one?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let L=length of each candle
And Let T=time(in hours) that will pass until the slow burning candle is exactly twice as long as the fast burning one
The fast burning candle burns at the rate of (1/6)L per hour
And the slow burning candle burns at the rate of (1/9)L per hour
Now, after T hours the slow burning candle is L-(1/9)L*T long
And the fast burning candle is L-(1/6)L*T long
We are told that the slow burning candle is now twice as long as the fast burning candle, so our equation to solve is:
L-(1/9)L*T=2(L-(1/6)L*T)) simplify
L-(1/9)L*T=2L-(2/6)L*T divide each term by L
1-(1/9)T=2-(2/6)T subtract 1 from and add (2/6)T to each side
1-1-(1/9)T+(2/6)T=2-1-(2/6)T+(2/6)T
-(2/18)T+(6/18)T=1
(4/18)T=1 multiply each side by 18
4T=18 divide each side by 4
T=4.5 hrs ----------------------time needed for slow burning candle to be exactly twice as long as the fast burning candle
CK
In 4.5 hours the slow burning candle is (L-(1/9)*4.5L)=(L-0.5L) units long
In 4.5 hours the fast burning candle is (L-(1/6)*4.5L)+(L-0.75L) units long
And we are told that:
(L-0.5L)=2(L-0.75L) or
0.5L=2(0.25)L
0.5L=0.5L

Hope this helps---ptaylor