Two candles of equal height are lit simultaneously. One burns down completely in 4 hours, while the other burns down completely in 3 hours. Assuming each burns at a constant rate, after how many hours will one candle be exactly twice as tall as the other?
2.4 hours (or 2 hours and 24 minutes)
Let the original height be 1. After t hours, candle 1 has height 1 - t/4 and candle 2 has height 1 - t/3. Setting 1 - t/4 = 2(1 - t/3) gives 1 - t/4 = 2 - 2t/3. Rearranging yields (2/3 - 1/4)t = 1, so (5/12)t = 1, which gives t = 12/5 = 2.4 hours.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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