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anonymous

  • one year ago

Robert bought 2 different candles. the ratio of short candle to the longer candle is 5 : 7. it is known that the longer candle when lighted can melt in 3.5 hours while the shorter candle when lighted can melt in 5 hours. now the two candles are lighted at the same time. after how many hours will the length of two candles be exactly equal ?

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  1. anonymous
    • one year ago
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    @ganeshie8

  2. anonymous
    • one year ago
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    |dw:1434959599826:dw|

  3. anonymous
    • one year ago
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    i sure the shrter one is more fat :)

  4. ganeshie8
    • one year ago
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    Haha is the answer 2 hours ?

  5. anonymous
    • one year ago
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    im asking this problem, so i dont know the answer. can you show how to get that ?

  6. ganeshie8
    • one year ago
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    Easy... Let \(5x\) = length of the short candle in meters \(7x\) = length of the longer candle in meters \(t\) = time elapsed in hours after the candles are lit

  7. ganeshie8
    • one year ago
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    rate of melting of short candle = \(\large \frac{5x ~\text{meters}}{5 \text{hours}} = x\text{ meters/hour}\) starting length of short candle = \(5x\) The length short candle after \(t\) hours is given by \[5x-x*t \tag{1}\]

  8. ganeshie8
    • one year ago
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    rate of melting of long candle = \(\large \frac{7x ~\text{meters}}{3.5 \text{hours}} = 2x\text{ meters/hour}\) starting length of short candle = \(7x\) The length longer candle after \(t\) hours is given by \[7x-2x*t \tag{2}\]

  9. ganeshie8
    • one year ago
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    set both equation equal to each other and solve \(t\)

  10. anonymous
    • one year ago
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    ok got it... thanks for your help

  11. ganeshie8
    • one year ago
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    weird, the time at which the candles get to same heights doesn't depend on their starting lengths

  12. dan815
    • one year ago
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    |dw:1434961190951:dw|

  13. dan815
    • one year ago
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    |dw:1434961425203:dw|

  14. dan815
    • one year ago
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    i dont know why i even change the ratio lol

  15. dan815
    • one year ago
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    heres a ssimple way

  16. dan815
    • one year ago
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    |dw:1434961663833:dw|

  17. dan815
    • one year ago
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    which is nice to look at, that the candle is burning exactly 2 times faster

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