Problem 3. We have two candles of different lengths and thicknesses. The longer and thinner candle burns completely in 3.5 hours, while the shorter and thicker candle burns in 5 hours. The candles were lit simultaneously, and after 2 hours of burning, their lengths were equal. By what percentage is the thinner candle longer than the thicker one?
Solution. In one hour, $\frac{2}{7}$ of the first (longer and thinner) candle burns, and $\frac{1}{5}$ of the second (shorter and thicker) candle burns. After two hours, $\frac{4}{7}$ of the first and $\frac{2}{5}$ of the second candle have burned. This means $\frac{3}{7}$ of the first and $\frac{3}{5}$ of the second candle remain. Since these lengths are equal, $\frac{1}{7}$ of the first candle is equal to $\frac{1}{5}$ of the second candle. Therefore, the first candle has a length of $7x$, and the second candle has a length of $5x$, so the thinner candle is $40\%$ longer than the thicker candle.