The Two Candles
Level
pending
Two candles have different thicknesses and lengths. The long one can burn 7/2 hours while the short one 5 hours. After 2 hours of burning, the candles are of equal length. Two hours ago, what fraction of the long candle's height was the short candle's height?
3/5
5/7
25/37
7/10
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1 solution
LONG CANDLE
in 7/2 hours, it burns fully
thus in 2 hours, it burns (2/7) X 2 part = 4/7 part
thus remaining part = 1 - (4/7) = 3/7 part
SHORT CANDLE
in 5 hours, it burns fully
thus in 2 hours, it burns (1/5) X 2 part = 2/5 part
thus remaining part = 1 - (2/5) = 3/5 part
Now, the problem states that after two hours of burning, their lengths are equal.
therefore,
3/7 of long candle = 3/5 of short candle
By solving the above equation, we can arrive at this:
(short candle) / (long candle) = 5/7
Therefore, the shorter candle is 5/7 the length of the longer candle. :)