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A candle is made of $17$ ounces of wax. When the candle is burning, the amount of wax in the candle decreases by $1$ ounce every $4$ hours. If $6$ ounces of wax remain in this candle, for many hours has it been burning?

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Exponential growth and decay: word problems

Full solution

Q. A candle is made of

17

ounces of wax. When the candle is burning, the amount of wax in the candle decreases by

1

ounce every

4

hours. If

6

ounces of wax remain in this candle, for many hours has it been burning?

Calculate wax burned: Calculate the total amount of wax that has been burned so far. $\newline$ Initial wax = $17$ ounces $\newline$ Remaining wax = $6$ ounces $\newline$ Wax burned = Initial wax - Remaining wax $\newline$ Wax burned = $17$ ounces - $6$ ounces $\newline$ Wax burned = $11$ ounces
Determine burning rate: Determine the rate at which the wax is burning. $\newline$ Wax burns at a rate of $1$ ounce every $4$ hours.
Calculate total hours burned: Calculate the total number of hours the candle has been burning. $\newline$ Hours burned = $\frac{\text{Wax burned}}{\text{Rate of wax burning}}$ $\newline$ Hours burned = $\frac{11 \text{ ounces}}{1 \text{ ounce}/4 \text{ hours}}$ $\newline$ Hours burned = $11 \times 4 \text{ hours}$ $\newline$ Hours burned = $44 \text{ hours}$

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