A twelve inch candle and an 18 inch candle are lit around 9 in the evening. The 12 inch candle burns 0.5 inches every hour. The eighteen inch candle burns a bit faster, at 2 inches every hour.

How many hours will it take for the candles to be the same height?

Write an equation to find the answer.

*Use 'h' as your variable.

Let's define the problem mathematically by representing the height of each candle as a function of time.

### Definitions:
- The initial height of the **12-inch candle** is 12 inches, and it burns at a rate of 0.5 inches per hour. 
  - After \( h \) hours, the height of the 12-inch candle will be:
    \[
    \text{Height of 12-inch candle} = 12 - 0.5h
    \]
  
- The initial height of the **18-inch candle** is 18 inches, and it burns at a faster rate of 2 inches per hour. 
  - After \( h \) hours, the height of the 18-inch candle will be:
    \[
    \text{Height of 18-inch candle} = 18 - 2h
    \]

### Setting up the equation:
To find when the candles will be the same height, we set these two expressions equal to each other:
\[
12 - 0.5h = 18 - 2h
\]

### Solving the equation:

1. First, subtract \( 12 \) from both sides:
   \[
   -0.5h = 6 - 2h
   \]

2. Add \( 2h \) to both sides to get all the \( h \) terms on one side:
   \[
   1.5h = 6
   \]

3. Divide both sides by 1.5 to isolate \( h \):
   \[
   h = \frac{6}{1.5} = 4
   \]

### Answer:
The candles will be the same height after **4 hours**.

Would you like more details, or do you have any questions?

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Here are 5 related questions for practice:
1. After how many hours will the 18-inch candle burn out completely?
2. What will the height of each candle be after 3 hours?
3. How much taller is the 18-inch candle than the 12-inch candle after 2 hours?
4. How many hours will it take for the 12-inch candle to burn out?
5. What if the burning rate of the 12-inch candle was increased to 1 inch per hour—when would they be the same height?

**Tip:** Always check if both sides of the equation balance after solving to ensure correctness.

A twelve inch candle and an 18 inch candle are lit around 9 in the evening. The 12 inch candle burns 0.5 inches every hour. The eighteen inch candle burns a bit faster, at 2 inches every hour. How many hours will it take for the candles to be the same height?

Learn how to solve a candle height problem where two candles burn at different rates. This problem demonstrates key algebraic concepts involving linear equations and is suitable for students in Grades 6-8. Follow the step-by-step solution to find when the candles will be the same height.

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