Question 1208637
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 {{{12-3x}}}.
For the second candle, every hour, the height decreases by 12/3=4. Therefore, after x hours, the height would be {{{12-4x}}}.
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(12-4x)}}}. Distributing the 2 on the right hand side gives {{{12-3x=24-8x.}}} Adding {{{8x}}} to both sides now gives {{{12+5x=24}}}. Subtracting 12 from both sides gives {{{5x=12}}}. Finally, dividing both sides by 5 gives {{{x=12/5}}}. Therefore, the answer is {{{12/5}}} hours.