Associated Topics || Dr. Math Home || Search Dr. Math

### Burning Candles

```
Date: 06/10/99 at 08:56:26
From: Ben Dixon
Subject: Algebra Problem

On Christmas Eve two candles, one of which is one inch longer than the
other, are lighted. The longer one is lighted at 4:30 and the shorter
one at 6:00. At 8:30 they are both the same length. The longer one
burns out at 10:30 and the shorter one at 10:00. How long was each
candle originally?

Thank you.
```

```
Date: 06/13/99 at 03:51:19
From: Doctor Floor
Subject: Re: Algebra Problem

Hi, Ben,

We have to assume that the candles shorten at a constant rate when
burning. Let us assume that the shorter one burns down S inches per
hour, and the longer one L inches per hour.

We know that the total length of the longer candle is 6L, because it
burns out in 6 hours. We also know that the shorter candle is 4S, as
it burns out in 4 hours. Since the longer candle is 1 inch longer than
the shorter one, we find the equation:

6L = 4S + 1   ..........[1]

We also know that at 8:30 the longer candle has burned for 4 hours,
and the shorter one for 2.5 hours. The remaining length of the longer
candle is 6L - 4L = 2L at that time, and the length of the shorter
candle is 4S - 2.5S = 1.5S. This gives the equation:

2L = 1.5S   .............[2]

When we multiply by three we find 6L = 4.5S. Insert this in [1], to
find:

4.5S = 4S + 1   (subtract 4S from both sides)
0.5S = 1        (multiply by 2)
S = 2

When we insert this in [2] you'll find that L = 1.5 (check it).

So the shorter candle originally was 4S = 8 inches, and the longer one
6L = 9 inches.

I hope this helped.

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search