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A $\frac{9}{2}$ -inch candle burns down in $9$ hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a $3$ -inch candle to burn down?

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Compare and convert customary units

Full solution

Q. A

\frac{9}{2}

-inch candle burns down in

9

hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a

3

-inch candle to burn down?

Given information: We are given that a $4.5$ -inch candle burns down in $9$ hours. We need to find out how long it would take for a $3$ -inch candle to burn down, assuming the rate of burning is directly proportional to the length of the candle.
Calculate rate: First, we establish the rate at which the $4.5$ -inch candle burns. We divide the length of the candle by the time it takes to burn down completely. $\newline$ Rate $= \frac{\text{Length of candle}}{\text{Time to burn}}$ $\newline$ Rate $= \frac{4.5 \text{ inches}}{9 \text{ hours}}$
Calculate rate using values: Now we calculate the rate using the values given. Rate = $\frac{4.5 \text{ inches}}{9 \text{ hours}} = 0.5 \text{ inches per hour}$
Determine time for $3$ -inch candle: Next, we use the rate to determine how long it will take for a $3$ -inch candle to burn down. We divide the length of the $3$ -inch candle by the rate of burning. $\newline$ Time to burn = Length of candle / Rate $\newline$ Time to burn = $\frac{3 \text{ inches}}{0.5 \text{ inches per hour}}$
Calculate time for $3$ -inch candle: Now we calculate the time it would take for the $3$ -inch candle to burn down. $\newline$ Time to burn = $\frac{3 \text{ inches}}{0.5 \text{ inches per hour}} = 6$ hours

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