algebra word problem

Question

A candle that has been burning for two minutes is eight inches long. That same candle is seven and one-quarter inches long after burning three minutes. Assume that the candle will burn at the same rate.

 

I have some of the answers already:

 

1. when will the candle burn out: ??minutes and 0 for inches

2. How long will the candle be 20 after it was list according to this algebraic  model: 20min, -5.5 inches

3. how long was the candle when it was lit: 0min, 9.5 inches

4. when will the candle be half of its original height: Minutes?, 4.75 inches

 

I also need the expression to this problem.

thank you.

Answer 1

Hi Celia,

 

If the candle burns at the same rate as it says in the problem we can create a relationship between the length of the candle and the time it burns

 

Let L = the length of the candle

Let m = minutes burned

 

 

we have two point of this relationship  (2,8)  (candle is 8 in after 2 minutes

and                                                  (3,7.25)  (candle is 7.25 after 3 minutes

 

find the change per minute (this becomes the slope of our linear equation

 

(8-7.25)/(2-3)

 

change per minute = slope = -.75

 

L = -.75m + c                   (so our length reduces .75 of an inch each minute

 

now find c

 

L = -.75(2) + c

 

8 = -1.5 + c

 

c = 9.5

 

our  relationship is 

 

L = -.75m + 9.5      (with this relationship you should be able to answer all of the questions

 

when m = 0

 

L = 0 + 9.5

 

When L = 4.75  we can find m

 

4.75 = -.75m + 9.5

 

-4.75 = -.75m

 

m = 6.3333 minutes

 

candle will burn out in twice that time  

 

m = 12.6667  minutes

 

 

Hope this helps