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Regard the candles as being of unit height then the first candle's height after time 't' is 1 - t/6 and the second candle's height is 1 - t/8.

When the first candle is half the height of the second candle then :

2(1 - t/6) = 1 - t/8 : 2 - t/3 = 1 - t/8 : 1 = t/3 - t/8 = 5t/24 :

t = 24/5 = 44/5 hours = 4 hours 48 minutes.

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