Question 1065529
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two candles of equal length are lit at the same time. one candle takes 6 hours to burn out and the other takes 3 hours. 
After how much time will the slower burning candle be exactly twice as long as the faster burning one? 
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Faster candle rate of burning is {{{L/3}}} of its length per hour.

Slower candle rate of burning is {{{L/6}}} of its length per hour.

The length of the remaining part for the faster candle is {{{L - (L/3)*t}}} after t hours.

The length of the remaining part for the slower candle is {{{L - (L/6)*t}}} after t hours.

The question asks about time t when Slower(t) = 2*Faster(t), or

{{{2*(L - (L/3)*t)}}} = {{{(L - (L/6)*t)}}} .


To solve for t, multiply both sides by {{{6/L}}}. You will get

{{{12*(1-t/3)}}} = {{{6*(1-t/6)}}},   or

12 - 4t = 6 - t  --->  12 - 6 = 4t - t  --->  6 = 3t  --->  t = 2.

<U>Answer</U>. After 2 hours.
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