Question 265216: Cara like candles. She also like mathematic and was thinking about using algebra to answer a question that she had about two of her candles. Her taller candle is 16 centimeters tall. each hour which it burns makes the candle lose 2.5 centimeter in height for each hour that it burns.
Cara need your help to determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. She wants to know what height the two candles would be at that time. If it is not possible, she want to know why. explain, use multiple representations, and justify your results.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! We need to know the height and burn rate of the 2nd candle
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Editing the problem with some additional information from your comment:
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taller candle is 16 centimeters tall. each hour which it burns makes the candle lose 2.5 centimeter in height for each hour that it burns.
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THe height of the 2nd candle in 12 centimeters, and the burn rate is 1.5 centimeters for each hour it burns.
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determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. She wants to know what height the two candles would be at that time.
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Let t = time when they are the same height (hrs)
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16 - 2.5t = 12 - 1.5t
16 - 12 = -1.5t + 2.5t
4 = t; this will occur in 4 hrs
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Finding the height of each candle after 4 hrs will prove this is true
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Substituting 4 for t in each equation
the 16cm candle
16 - 2.5t =
16 - 4(2.5) =
16 - 10 = 6 cm
and for the 12cm candle
12 - 1.5t =
12 - 4(1.5) =
12 - 6 = 6 cm; That's the height of the two candles and we proved it.
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