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A 6-inch candle burns down in 4 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 
4(1)/(2)-inch candle to burn down?
Answer: hours

A 66-inch candle burns down in 44 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 412 4 \frac{1}{2} -inch candle to burn down?\newlineAnswer: hours

Full solution

Q. A 66-inch candle burns down in 44 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 412 4 \frac{1}{2} -inch candle to burn down?\newlineAnswer: hours
  1. Given Information: We are given that a 66-inch candle burns down in 44 hours. We need to find out how long it would take for a 4.54.5-inch candle to burn down, assuming the burn rate is directly proportional to the length of the candle.
  2. Calculate Burn Rate: First, let's establish the rate at which the 66-inch candle burns. We divide the length of the candle by the time it takes to burn down.\newlineRate = Length / Time = 6 inches4 hours=1.5 inches/hour.\frac{6 \text{ inches}}{4 \text{ hours}} = 1.5 \text{ inches/hour}.
  3. Find Time for 44.55-inch Candle: Now, we have a 4.54.5-inch candle. We want to find the time it takes to burn down at the same rate of 1.51.5 inches/hour.\newlineTime = Length / Rate = 4.54.5 inches / 1.51.5 inches/hour.
  4. Final Calculation: Perform the division to find the time.\newlineTime = 4.5inches1.5inches/hour=3hours.\frac{4.5 \, \text{inches}}{1.5 \, \text{inches/hour}} = 3 \, \text{hours}.

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