Answer :
To determine how many hours it will take for a 5-inch candle to burn down by 4 inches, we will follow a step-by-step approach:
1. Determine the burn rate per hour:
- We know that a 5-inch candle burns down completely in 3 hours.
- Therefore, the rate at which the candle burns down can be calculated using the formula:
[tex]\[ \text{Burn rate per hour} = \frac{\text{Total height of the candle}}{\text{Total hours to burn completely}} \][/tex]
Substituting the given values:
[tex]\[ \text{Burn rate per hour} = \frac{5 \text{ inches}}{3 \text{ hours}} = \frac{5}{3} \text{ inches per hour} \][/tex]
2. Calculate the time to burn 4 inches:
- To find the time required to burn 4 inches, we need to divide the number of inches to be burned by the burn rate per hour:
[tex]\[ \text{Time to burn 4 inches} = \frac{\text{Inches to be burned}}{\text{Burn rate per hour}} \][/tex]
Substituting the values:
[tex]\[ \text{Time to burn 4 inches} = \frac{4 \text{ inches}}{\frac{5}{3} \text{ inches per hour}} = 4 \times \frac{3}{5} = \frac{12}{5} \text{ hours} \][/tex]
3. Express the result in different formats:
- As a decimal:
[tex]\[ \frac{12}{5} = 2.4 \text{ hours} \][/tex]
- As a mixed number:
[tex]\[ \frac{12}{5} = 2 \frac{2}{5} \text{ hours} \][/tex]
- As an improper fraction:
[tex]\[ \frac{12}{5} \text{ hours} \][/tex]
Therefore, it will take [tex]\(2.4\)[/tex] hours (or [tex]\(2 \frac{2}{5}\)[/tex] hours, or [tex]\(\frac{12}{5}\)[/tex] hours) for the candle to burn 4 inches.
1. Determine the burn rate per hour:
- We know that a 5-inch candle burns down completely in 3 hours.
- Therefore, the rate at which the candle burns down can be calculated using the formula:
[tex]\[ \text{Burn rate per hour} = \frac{\text{Total height of the candle}}{\text{Total hours to burn completely}} \][/tex]
Substituting the given values:
[tex]\[ \text{Burn rate per hour} = \frac{5 \text{ inches}}{3 \text{ hours}} = \frac{5}{3} \text{ inches per hour} \][/tex]
2. Calculate the time to burn 4 inches:
- To find the time required to burn 4 inches, we need to divide the number of inches to be burned by the burn rate per hour:
[tex]\[ \text{Time to burn 4 inches} = \frac{\text{Inches to be burned}}{\text{Burn rate per hour}} \][/tex]
Substituting the values:
[tex]\[ \text{Time to burn 4 inches} = \frac{4 \text{ inches}}{\frac{5}{3} \text{ inches per hour}} = 4 \times \frac{3}{5} = \frac{12}{5} \text{ hours} \][/tex]
3. Express the result in different formats:
- As a decimal:
[tex]\[ \frac{12}{5} = 2.4 \text{ hours} \][/tex]
- As a mixed number:
[tex]\[ \frac{12}{5} = 2 \frac{2}{5} \text{ hours} \][/tex]
- As an improper fraction:
[tex]\[ \frac{12}{5} \text{ hours} \][/tex]
Therefore, it will take [tex]\(2.4\)[/tex] hours (or [tex]\(2 \frac{2}{5}\)[/tex] hours, or [tex]\(\frac{12}{5}\)[/tex] hours) for the candle to burn 4 inches.
