SOLUTION: Hello! I would appreciate it if you could help me solve this word problem: Two candles of the same height are lit at the same time. The first is consumed in four hours, the seco

Question 1208637: Hello! I would appreciate it if you could help me solve this word problem:
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?
Found 3 solutions by Shin123, josgarithmetic, timofer:
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
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.
For the first candle, every hour, the height decreases by 12/4=3. Therefore, after x hours, the height would be .
For the second candle, every hour, the height decreases by 12/3=4. Therefore, after x hours, the height would be .
Now, we need to find the time such that the first candle had twice the height of the second. This gives us the equation . Distributing the 2 on the right hand side gives Adding to both sides now gives . Subtracting 12 from both sides gives . Finally, dividing both sides by 5 gives . Therefore, the answer is hours.
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!

CANDLE BURN RATE TIME LENGTH of CANDLE First d/4 x d-(d/4)x Second d/3 x d-(d/3)x

Question seems to need the "length of candles" to be as .

If divide left and right by d, then ;

multiply left and right sides by 12;

and this is 2 and two-fifths hours

or two hours twenty-four minutes.
Answer by timofer(106)   (Show Source): You can put this solution on YOUR website!
You can take the original length of each candle to both be a unit of 1, for 1 candle length. Then for some expected time, since both are started at the same time, candle #1 will be and candle #2 will be .

You would have then .
Simplify this and solve for the time, x.
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