SOLUTION: Two candles are the same length but are made of different waxes. One will burn down in four hours, and the other in five. If they are lighted at the same time, in how many hours wi

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Question 165043: Two candles are the same length but are made of different waxes. One will burn down in four hours, and the other in five. If they are lighted at the same time, in how many hours will one be three times as long as the other? (Hint: chose a length for the two candles.)
Please help me!!!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let c="length of candles"

a candle that burns for h hours will burn t/h of the length in time t
__ the REMAINING length will be c[1-(t/h)]

the slower burning candle will be the longest

c[1-(t/5)]=3c[1-(t/4)] __ dividing by c and distributing __ 1-(t/5)=3-(3t/4)

adding (3t/4)-1 __ (3t/4)-(t/5)=2 __ multiplying by LCD (20) __ 15t-4t=40 __ 11t=40 __ t=40/11