Two candles

small_unicorn

Two candles have different lengths and thicknesses. The long one can burn $3\frac{1}{2}$ hours; the short one, 5 hours.
After 2 hours burning, the candles are equal in length. Two hours ago, what fraction of the long candle's height gave the short candle's height ?

from book "The Moscow puzzles" by Boris A. Kordemsky

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Moose

**Posted:** Tue Nov 03, 2009 3:26 pm

$LaTeX$

Let x and y be the length of the long and short candles respectively. After 2 hours, $2\div3\frac{1}{3}=\frac{4}{7}x$ has burned, and $\frac{2}{5}y$ has burned. This leaves $\frac{3}{7}x=\frac{3}{5}y$ . Thus the short candle had a height that was $\boxed{\frac{5}{7}}$ of the long one.

**Posted:** Tue Nov 03, 2009 3:31 pm

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small_unicorn

**Posted:** Tue Nov 03, 2009 3:51 pm