Question 126685
One type of beeswax candle burns up in 6 hours. Another paraffin candle of the same length burns up in 9 hours. If both candles are lit at the same time, how much time will pass before one is twice as long as the other?
:
Choose a convenient length; 18" is a good length (has a lot of factors)
:
The b candle burns at a rate of 18/6 = 3" per/hr
The p candle burns at a rate of 18/9 = 2" per/hr
:
Let t = time (in hrs) elapsed for p to be twice as long as b
:
18 - 2t  =  2(18 - 3t)
:
18 - 2t = 36 - 6t
:
-2t + 6t = 36 - 18
:
4t = 18
t = {{{18/4}}}
t = 4.5 hrs
:
:
Check solution:
18 - 4.5(2) = 9"
18 - 4.5(3) = 4.5"