Two candles of the same height are lighted at the same time. The first is consumed in 8 hours and the second in 6 hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second? (i.e., the ratio between the first and second candles becomes 2 : 1)
SOLUTION:
Let the candles be A and B with height 24 meters each (LCM of 8 and 6)
A B
Completely Burns in 8 hr 6 hr
in 1 hr Candle burns by 3 4 (Divide height by time)
After burning for time, T,
Heights reduced by 3T 4T
Remaining Height is 24 - 3T 24 - 4T
It is Given that, The ratio of heights will be 2 : 1, on applying this
(24 - 3T) : (24 - 4T) = 2 : 1
On solving for T, we will get T = 24/5 = 4 hours 48 mins.
So, after 4 hr 48 mins of lighting, the candles height will be in the ratio of 2:1.