Candle in the Wild(Part 1)

Algebra Level pending

Two candles have the same height but different diameters. It takes one candle 3 hours to burn out and the other 4 hours to burn out. At what times must the candles be lit for the ratio of the heights to be 1 : 2 at 3pm?

11.35pm 12.35pm 11.36pm 12.36pm

Sin Ndt by SIN NDT , 14, Vietnam

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1 solution

Let the length of each candle be L L . Let the final lengths of the two candles be x x and 2 x 2x respectively. Then 3 ( 1 − x L ) = 4 ( 1 − 2 x L ) ⟹ x L = 1 5 ⟹ 3 ( 1 − x L ) = 12 5 3\left (1-\dfrac{x}{L}\right) =4\left (1-\dfrac{2x}{L}\right) \implies \dfrac{x}{L}=\dfrac{1}{5}\implies 3\left (1-\dfrac{x}{L}\right) =\dfrac{12}{5} . Therefore the time during which the candles burnt is 12 5 \dfrac{12}{5} hrs. or 2 2 hrs. 24 24 min. Hence the required answer is 12.36 12.36 P. M.

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