Algebra word problem?
Two candles of the same height are lit at the same time. One of the candles burns out in 4h. The other candle burns out in 3h. How long after lighting was the first candle twice as high as the second?
Please show work.
Two candles of the same height are lit at the same time. One of the candles burns out in 4h. The other candle burns out in 3h. How long after lighting was the first candle twice as high as the second?
Please show work.
Comments
Let the candle height be 1 unit, and assume that t hours after lighting the first candle is twice as high as the second.
Rate of burning of 1st candle = 1/4 per hour
Rate of burning of 3nd candle = 1/3 per hour
After t hours, 1st candle height remains = 1 - (1/4) t
After t hours, 2nd candle height remains = 1 - (1/3) t
Per condition, 1 - (1/4) t = 2*[1 - (1/3) t] = 2 - (2/3) t
(2/3) t - (1/4) t = 2 - 1 or t = 12/5 hours