Candle P and candle Q of equal length are lighted at the same time and burning until candle P is twice as long as candle Q. Candle P is designed to fully burn in 8 hours while candle Q for 4 hours. How long will they be lighted?

Question

anonymous · Answer

I got 8/3 hours

Did you try with something?

anonymous · Answer

How?

anonymous · Answer

First of all for all written question you need to write equations first. 
However for equations you need to decide the variables. 

What should be the variables of this problem?

anonymous · Answer

Was that a rate problem?

anonymous · Answer

No

anonymous · Answer

Can you try to answer my question? What are the unknowns?

anonymous · Answer

Length of the candles and the required is the time it would take them to be finished. Is there any tricky part in the question?

anonymous · Answer

Not so tricky. And yes those are what we need sort of.

anonymous · Answer

Let us translate English to Maths now

anonymous · Answer

In order to do so we need to label clearly the unknowns. 
Let t be the time needed to reach the given state. 
Let l be the length of the candles at the start.
Let x be the length of candle P at any given time t. 
Let y be the length of candle Q at any time t.

anonymous · Answer

Now we know that at time t one candle is double the length than the other. 
Thus 
x=2y

anonymous · Answer

We need a formula for x and y now. This is the tricky part I assume

anonymous · Answer

$$x=l-t \frac{ l }{ 8 }$$

anonymous · Answer

$$y=l-t \frac{ l }{ 4 }$$

anonymous · Answer

If you solve this system of equations. You will get your answer.

anonymous · Answer

This is the method I use when facing written maths problems. 
I hope it helped.

anonymous · Answer

So basically, the equation is based on lengths, not time? I see!.. Thanks, Merci!

anonymous · Answer

It helped a lot!

anonymous · Answer

When you solve it l will drop out and you will get to t=something