An algebra problem by A Former Brilliant Member

Algebra Level 3

Two candles of the same height are lit at the same time. The first is consumed in 4 hours and the second in 3 hours. Assuming that each candle burns at a constant rate, in how many hours after being lit is the first candle twice the height of the second?

1\dfrac{1}{2}

hr None of these.

2

\dfrac{3}{4}

2\dfrac{2}{5}

1 solution

Chew-Seong Cheong
Apr 25, 2016

Let the height of the two candles be $h$ , then the rate of burning of the first and second candles are $\dfrac{h}{4}$ and $\dfrac{h}{3}$ respectively. Let the time when the first candle is twice the height of the second after the candles started burning be $t$ . Then we have:

$\begin{aligned} h- \frac{h}{4}t & = 2 \left(h - \frac{h}{3}t \right) \\ \implies 1- \frac{1}{4}t & = 2 - \frac{2}{3}t \\ \dfrac{5}{12} t & = 1 \\ \implies t & = \frac{12}{5} = \boxed{2\dfrac{2}{5} \text{ hr}} \end{aligned}$

An algebra problem by A Former Brilliant Member

1 solution

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