Question 72978
2 candles with equal lengths. Both candles are lit at the same time. Candle A burns out at 9 hours. Candle B burns out at 6 hours. At what time is the slower burning candle twice as long as the faster burning candle? 
:
For convenience let's assign a length of 9" to the candles
That means:
Candle A burns 1"/hr and candle B burns 1.5"/hr
:
Let t = hrs until A is twice as long as B
An equation:
9 - 1t = 2(9 - 1.5t)
9 - t = 18 - 3t
-t + 3t = 18 - 9
2t = 9
t = 4.5 hrs
:
Check:
 candle A after 4.5 hrs: 9 - (4.5 * 1) = 4.5"
 candle B after 4.5 hrs: 9 - (4.5 * 1.5) = 9 - 6.75 = 2.25"