Two candles of same height are lighted at the same time. The first is consumed in 3 hours and second in 2 hours. Assuming that each candles burns at a constant rate, in how many hours after being lighted, the ratio between the first and second candles becomes 2:1?
Question
Two candles of same height are lighted at the same time. The first is consumed in 3 hours and second in 2 hours. Assuming that each candles burns at a constant rate, in how many hours after being lighted, the ratio between the first and second candles becomes 2:1?
Solution
Let's denote the height of each candle as H.
Since the first candle burns completely in 3 hours, it burns at a rate of H/3 per hour.
Similarly, the second candle burns at a rate of H/2 per hour.
We want to find the time t at which the ratio of the heights of the first and second candles is 2:1.
We can set up the equation as follows:
(H - t*(H/3)) / (H - t*(H/2)) = 2/1
Solving this equation for t gives us:
2*(H - t*(H/2)) = H - t*(H/3)
2H - tH = H - t(H/3)
H = t*H/3
t = 3 hours
So, the ratio between the first and second candles becomes 2:1 three hours after being lighted.
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