Consider two candles which have the same height. Each candle burns at a consistent rate (but the two candles have different burn rate). The first one melts completely in 5 hours, and the second one melts completely in 3 hours.
If they are lit at the same time, after how many minutes will the first one be thrice as long as the second one?
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Let the length of candles be 'L' units.
Candle 1
: It takes 3 hrs to completely melt down i.e. "L" length of candle melts down in 3 hrs
Thus in time "t" hrs length of candle melted:
3
L
×
t
Length of candle left:
L
−
3
L
×
t
Candle 2
: It takes 5 hrs to completely melt down i.e. "L" length of candle melts down in 5 hrs
Thus in time "t" hrs length of candle melted:
5
L
×
t
Length of candle left:
L
−
5
L
×
t
It is given that at time "t" length of candle 2 is 3 times the length of candle 1. Hence we write,
L − 5 L × t = 3 ( L − 3 L × t )
On solving, we get t = 4 1 0 hrs = 1 5 0 m i n s
Very clear solution! +1
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Let us assume that the length of the candles is 1.
The first candle melts 3 0 0 1 in one minute.
The second candle melts 1 8 0 1 in one minute.
If after t minutes, the length of the first candle is thrice the length of the second candle, then we have
3 ( 1 − 1 8 0 t ) = ( 1 − 3 0 0 t ) .
Solving this equation, we get that 3 0 0 4 t = 2 , or that t = 1 5 0 .