A few days ago
Two candles and time?
Two candles of equal length are lighted at noon. One candle takes 9 hours to burn out, and the other takes 6 hours to burn out. At what time will the slower-burning candle be exactly twice as long as the faster-burning one?
I’ve tried to determine their ‘work rate’ and multiply it by ‘x’ time, but it did not work for me. Could somebody show me the light? Thanks!
Top 1 Answers
A few days ago
Favorite Answer
Candle A takes 9hr. to burn out. Therefore 1/9 of its length burns each hour.
Candle B takes 6hr. Therefore 1/6 of its length burns each hour.
The fraction of candle A which is left after t hours is 1 – (t/9), and the fraction of candle B left is 1 – (t/6).
Therefore if t hours is the required time:
1 – t/9 = 2(1 – t/6)
Multiplying by 9:
9 – t = 18 – 3t
2t = 9
t = 9/2.
The required time is 9/2 hr.
Check:
After 9/2hr, the fraction of A left is 1 – 1/2 = 1/2.
The fraction of B left is 1 – 9/(2*6) = 1/4.
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