document.write( "Question 1208637: Hello! I would appreciate it if you could help me solve this word problem:\r
\n" ); document.write( "\n" ); document.write( "Two candles of the same height are lit at the same time. The first is consumed in four hours, the second in three hours. Assuming that each candle burns at a constant rate, how many hours after being lit was the first candle twice the height of the second? \n" ); document.write( "

Algebra.Com's Answer #847014 by Shin123(626) $\"\"$ $\"About$

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Note that the exact height of the candles doesn't matter, since the candles burn at a rate proportional to their height (and the candles both have the same height). So we can assign a value to the height. To make computations easier, let the common height be 12.
\n" ); document.write( "For the first candle, every hour, the height decreases by 12/4=3. Therefore, after x hours, the height would be $\"12-3x\"$ .
\n" ); document.write( "For the second candle, every hour, the height decreases by 12/3=4. Therefore, after x hours, the height would be $\"12-4x\"$ .
\n" ); document.write( "Now, we need to find the time such that the first candle had twice the height of the second. This gives us the equation $\"12-3x=2%2812-4x%29\"$ . Distributing the 2 on the right hand side gives $\"12-3x=24-8x.\"$ Adding $\"8x\"$ to both sides now gives $\"12%2B5x=24\"$ . Subtracting 12 from both sides gives $\"5x=12\"$ . Finally, dividing both sides by 5 gives $\"x=12%2F5\"$ . Therefore, the answer is $\"12%2F5\"$ hours. \n" ); document.write( "

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