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Three candles which can burn, 60 minutes, 80 minutes and 100 minutes respectively are lit at different times...

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Three candles which can burn, 60 minutes, 80 minutes and 100 minutes respectively are lit at different times. All the candles are burning simultaneously for 30 minutes, and there is a total of 40 minutes in which exactly one is burning. For how many minutes are exactly two candles burning?

posted Jul 15, 2016 by anonymous

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1 Answer

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55 minutes.
The total burn time of the candles = 60 + 80 + 100 = 240 minutes.
During that burn time either one, two or three candles are burning.
During 30 minutes all three candles burn = 90 minutes burn time.
During 40 minutes only one candle burns = 40 minutes burn time.
That leaves (240 - 90 - 40 = ) 110 minutes of burn time during which two candles are burning
=> 110 / 2 = 55 minutes long.

answer Jul 17, 2016 by Jcm
So u r saying there are 2 candles with burn time 55+30(85) min. But there is only one candle has length sufficient for 85 min. So u should reconsider ur solution
My solution is correct. You make the incorrect assumption that the 55 min 2 candle burn time has to come from the same candles. This is not so.
Let's say candle A = 60 minutes.
Candle B = 80 minutes.
Candle C = 100 minutes.
We lit candle B and let it burn for 25 minutes (25 min 1 candle).
We then lit candle C and let them together burn for 25 minutes (25 min 2 candles).
We then lit candle A. After 30 minutes candle B is gone (30 min 3 candles)
After another 30 minutes candle A is gone (30 min 2 candles).
After another 15 candle C is also gone (15 min 1 candle).
This gives a total of 40 min 1 candle + 55 min 2 candles + 30 min 3 candles.

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