Two candles are lit at the same moment. A fog hides them for hours
Mr. Gubbins lights two candles of equal length at the same moment: one would burn itself out, alone, in exactly four hours, the other in exactly five. A thick fog then rolls in and he can't check on them. When it finally clears and he puts both candles out, he notices that the stub of one candle is exactly four times the length of the stub of the other. For how long had the candles been burning?
Reveal the answer
Three hours and forty-five minutes. At that point the four-hour candle has one-sixteenth of its original length left, and the five-hour candle has four-sixteenths, exactly a 1:4 ratio. Henry Dudeney published this as 'Mr. Gubbins in a Fog' in Amusements in Mathematics (1917).
— Henry Ernest Dudeney, Amusements in Mathematics — Thomas Nelson & Sons, 1917
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