Two candles of equal length are lit at the same time. One candle takes 6 hours to burn out, and the other takes 9 hours to burn out. After how much time will the slower burning candle be exactly twice as long as the faster burning one?
Two candles of equal length are lit at the same time.
One candle takes 6 hours to burn out, and the other takes 9 hours to burn out.
After how much time will the slower burning candle be exactly twice as long as the faster burning one?
\(\begin{array}{|rcll|} \hline \text{Rest fast candle}&=& 1Candle - \dfrac{1candle}{6h}\times t \\ \text{Rest slow candle}&=& 1Candle - \dfrac{1candle}{9h}\times t \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline 2\times \text{Rest fast candle } &=& \text{Rest slow candle} \\\\ 2\times \left( 1Candle - \dfrac{1candle}{6h}\times t\right) &=& 1Candle - \dfrac{1candle}{9h}\times t \\\\ 2 - \dfrac{2}{6}\times t &=& 1 - \dfrac{1}{9}\times t \\\\ 2 - \dfrac{1}{3}\times t &=& 1 - \dfrac{1}{9}\times t \\\\ \dfrac{1}{3}\times t- \dfrac{1}{9}\times t &=& 1 \\\\ \dfrac{(9-3)}{3*9}\times t &=& 1 \\\\ \dfrac{6}{3*9}\times t &=& 1 \\\\ \dfrac{2}{9}\times t &=& 1 \\\\ t &=& \dfrac{9}{2} \\\\ \mathbf{t} &=& \mathbf{4.5~ hours} \\ \hline \end{array}\)