Question

Two candles of equal length are lit at the same time. One candle takes 6 hours to burn out, and the other takes 9 hours to burn out. After how much time will the slower burning candle be exactly twice as long as the faster burning one?

Answer 1

Answer:

4.5 hours

Step-by-step explanation:

Two candles of equal length. Let h cm be the length of each candle.

1st candle:

It takes 6 hours to burn out, then $\dfrac{h}{6}\ cm/h$ is the burning rate of the first candle.

2nd candle:

It takes 9 hours to burn out, then $\dfrac{h}{9}\ cm/h$ is the burning rate of the second candle.

In x hours, the first candle is $h-\dfrac{h}{6}x$ cm long and the second candle is $h-\dfrac{h}{9}x$ cm long.

The slower burning candle (the second candle) will be exactly twice as long as the faster burning candle (the first candle) in

$h-\dfrac{h}{9}x=2\left(h-\dfrac{h}{6}x\right)\\ \\1-\dfrac{x}{9}=2-\dfrac{x}{3}\\ \\\dfrac{x}{3}-\dfrac{x}{9}=2-1\\ \\\dfrac{2x}{9}=1\\ \\2x=9\\ \\x=4.5\ hours$