To create a proportional equation for the amount of the candle that has burned away in terms of time, we start by establishing the relationship between the length of the candle, the time it burns, and the amount burned.
We know:
- The original length of the candle is 33 inches.
- The candle burns down completely in 12 hours.
First, we need to find the rate at which the candle burns. The rate of burn can be calculated as follows:
\[ \text{Rate of burn} = \frac{\text{Total length}}{\text{Total time}} = \frac{33 \text{ inches}}{12 \text{ hours}} \approx 2.75 \text{ inches per hour} \]
Next, we want to express \( b \) (the amount of the candle that has burned away) in terms of \( t \) (the time in hours). Since the amount burned away increases as time passes, we can set up the equation:
\[ b = \text{Rate of burn} \times t \]
Substituting the rate we calculated:
\[ b = 2.75t \]
So the proportional equation that represents how much of the candle has burned away at any time \( t \) is:
\[ b = 2.75t \]