Question

A candle is lit and burns at a constant rate of change until it is completely burned. When the candle has been burning for 2.7 hours it is 14.3 inches tall and when it has been burning for 7.1 hours it is 4.2 inches tall. At what constant rate did the candle burn?

Answer 1

2.29 inches/hour

Explanation:

Given that the candle burns at a constant rate.

After time 2.7 hours, candle was 14.3 inches tall.

After time 7.1 hours, candle was 4.2 inches tall.

To find:

The constant rate at which the candle burn.

Solution:

Let the length be represented by
`l` and time be represented by
`t`.

Let the constant rate be
`m`.

and the initial length be
`L.`

The equation can be written as:

`l =mt+L`

At
`t` = 2.7 hours ,
`l` = 14.3 inches

`14.3 =2.7m+L ..... (1)`

At
`t` = 7.1 hours ,
`l` = 4.2 inches

`4.2 =7.1m+L ..... (2)`

Equation (1) minus (2):

`10.1=-4.4m\\\Rightarrow m = - 2.29\ inches/hour`

The candle burns at the rate of 2.29 inches/hour.