A 7.5-inch candle burns down in 10 hours. Assuming the candles are the same thickness and make, how long would it take a 4.5-inch candle to burn down?

Steps to Solve

1. Set up the ratio based on candle lengths

To find out how long it will take for the 4.5-inch candle to burn, we can set up a ratio based on the lengths of the candles and their burn times.

We know:

• Length of the larger candle: ( 7.5 ) inches
• Burn time of the larger candle: ( 10 ) hours
• Length of the smaller candle: ( 4.5 ) inches
• Burn time of the smaller candle: ( x ) hours (this is what we want to find)

We can express this relationship as: $$\frac{7.5 \text{ inches}}{10 \text{ hours}} = \frac{4.5 \text{ inches}}{x \text{ hours}}$$

2. Cross-multiply to solve for ( x )

Now we will cross-multiply to solve for ( x ): $$ 7.5 \cdot x = 4.5 \cdot 10 $$

3. Calculate ( x )

Now we perform the multiplication on the right. $$ 7.5x = 45 $$

Next, divide both sides by ( 7.5 ): $$ x = \frac{45}{7.5} $$

Calculating this gives: $$ x = 6 $$

So, it will take ( 6 ) hours for the 4.5-inch candle to burn down.