17. Julio has two cylindrical candles with different heights and diameters. The two candles burn wax at the same uniform rate. The first candle lasts 6 hours, while the second candle lasts 8 hours. He lights both candles at the same time and three hours later both candles are the same height. What is the ratio of their original heights?
A $4: 3$
B $8: 5$
C 5:4
D $3: 5$
E 7:3
17. C Let the original heights of the first and second candles be $x$ and $y$ respectively. Since the first candle lasts six hours, after three hours its height is $\frac{1}{2} x$. Similarly, since the second candle lasts eight hours, after three hours its height is $\frac{5}{8} y$. After three hours the two candles have the same height and hence $\frac{1}{2} x=\frac{5}{8} y$. Therefore $\frac{x}{y}=\frac{5}{4}$ and hence the ratio of their original heights is $5: 4$.