When were the two candles the same height?

Question

Two candles start at the same height. Candle A burns steadily and lasts 6 hours. Candle B, the same height, burns steadily and lasts 4 hours. Candle A is lit at noon. Candle B is lit one hour later, at 1 pm. At what time are the two candles the same height?

Accepted Answer

At 3 pm, three hours after candle A was lit (two hours after candle B was lit). Let t be the number of hours after noon, with starting height 1. - Candle A: height 1 minus t/6. - Candle B (lit at t = 1): height 1 minus (t minus 1)/4, valid for t at least 1. Set them equal: 1 minus t/6 = 1 minus (t minus 1)/4 so t/6 = (t minus 1)/4. Multiply both sides by 12: 2t = 3(t minus 1) = 3t minus 3, giving t = 3. Check. At 3 pm candle A has burned 3 of its 6 hours, so it is half height. Candle B has burned 2 of its 4 hours, so it is also half height. Equal. Why there is exactly one such moment. Before …

When were the two candles the same height?

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