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Deepak Bora
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To fill a swimming pool two pipes are to be used . If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter is used for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool separately , if the pipe of the smaller diameter takes 10 hours more than the pipe of the larger diameter to fill the pool

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Word problems on quadratic equation in one variable .

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  1. Let time taken by the pipe with larger diameter(A) = x hours,

    And time taken by the pipe with smaller diameter (B)= (x+10) hours,

    ∴ A’s one hour work = 1/x

    B’s one hour work = 1/(x+10)

    Work done by A in 4 hour = 4/x

    Work done by B in 9 hours = 9/x+10

    According to the question

    4/x + 9/x+10 = 1/2

    After Taking LCM & cross multiplying

    2(13x+40) = x² + 10x

    x² -16x-80 = 0

    x² -20x+4x-80=0

    x(x-20) +4(x-20)= 0

    (x-20)(x+4)= 0

    If (x-20)= 0    & (x+4) = 0

    ∴ x= 20        & x = -4

    Because time taken can’t be negative,

    ∴ timextime taken by the pipe with larger diameter (x) =  20 hours

    And time taken by the pipe with smaller diameter (x+10) = 30 hours

     

     

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