Solving Candle Burn Time Problem with Algebra

[Vuldoraq]

Homework Statement

Two candles A and B are 8cm and 14cm long, respectively, and are lit at hte same time. If candle B burns twice as fast as candle A, how long are they when their lengths are the same. How long is candle A when candle B burns out?

Homework Equations

Not sure.

The Attempt at a Solution

I drew a table of length's for equal time width's. So when A is 7cm ling B will be 12cm long etc. I found that they would be 2cm a piece when they are the same length and that candle A would be 1cm long when candle B burns out. Is this correct?

More importantly how do I answer this question algebraically? The above seems to me like the dumb approach, but I just can't see how to model the problem.

Any help would be much appreciated!

 

[LowlyPion]

Homework Statement

Two candles A and B are 8cm and 14cm long, respectively, and are lit at hte same time. If candle B burns twice as fast as candle A, how long are they when their lengths are the same. How long is candle A when candle B burns out?

Homework Equations

Not sure.

The Attempt at a Solution

I drew a table of length's for equal time width's. So when A is 7cm ling B will be 12cm long etc. I found that they would be 2cm a piece when they are the same length and that candle A would be 1cm long when candle B burns out. Is this correct?

More importantly how do I answer this question algebraically? The above seems to me like the dumb approach, but I just can't see how to model the problem.

Any help would be much appreciated!

Your answers are right. Let LB = Length Burned of A

8 - LB = Height(a)

14 - 2*LB = Height(b)

When Heights are equal LB = 6, Height(a) = 2
When Height(b) = 0, T = 7, then Height(a) = 8 - 7 = 1

 

[Vuldoraq]

Thanks a million LowlyPion. I kept trying to use series sums etc, but I just couldn't get it to work. Your answer is much simpler!

Vuldoraq