To model the length of the candle remaining unburned over time, we can first determine the rate at which the candle burns.

1. Initial length of the candle: $L_0 = 10$ inches
2. Length after 4 hours: $L(4) = 5$ inches

The candle burned 5 inches in 4 hours, so the rate of burning can be calculated as follows:

$\text{Rate of burn} = \frac{L_0 - L(4)}{4 \text{ hours}} = \frac{10 - 5}{4} = \frac{5}{4} \text{ inches per hour}$

The equation for the length $L(t)$ of the candle remaining after $t$ hours can be expressed as:

$L(t) = L_0 - \text{(Rate of burn)} \times t$

Substituting in the values:

$L(t) = 10 - \frac{5}{4}t$

Thus, the equation for the length of the candle remaining unburned, in inches, $L(t)$ after $t$ hours is:

$L(t) = 10 - \frac{5}{4}t$

Questions:

1. How long will it take for the candle to completely burn down?
2. What will be the height of the candle after 6 hours?
3. If the candle burns for 10 hours, how much will be left?
4. Can you describe how the rate of burn affects the candle's total burn time?
5. What happens to the equation if the candle burns at a different rate?

Tip:

When creating linear equations based on real-world scenarios, always ensure to identify key points and rates of change for accurate modeling.