Question 747824
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Perhaps the solution is easier to understand if we work with the fraction of each candle that remains after a certain number of hours, instead of the length of each candle.<br>
First candle:
burns completely in 5 hours
fraction of the candle that burns each hour: {{{1/5}}}
fraction of the candle that burns in t hours: {{{(1/5)t}}}
fraction of the candle that remains after t hours: {{{1-(1/5)t}}}<br>
Second candle:
burns completely in 4 hours
fraction of the candle that burns each hour: {{{1/4}}}
fraction of the candle that burns in t hours: {{{(1/4)t}}}
fraction of the candle that remains after t hours: {{{1-(1/4)t}}}<br>
Since the candles are the same length, the first candle is 4 times as long as the second when the fraction of the first candle that remains is 4 times the fraction of the second candle that remains:<br>
{{{1-(1/5)t=4(1-(1/4)t)}}}
{{{1-(1/5)t=4-t}}}
{{{(4/5)t=3}}}
{{{t=15/4}}}<br>
ANSWER: the length of the first candle is 4 times the length of the second candle after 15/4 hours, or 3 3/4 hours, or 3 hours and 45 minutes.<br>