asf asked in 科學及數學數學 · 6 years ago

F.4 Maths Help !!測驗用 20 marks

Update:

117 ans : 30 hours

118 ans: 10 days

聽日測啦,大家幫幫手啊,謝謝

1 Answer

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  • wy
    Lv 7
    6 years ago
    Favorite Answer

    117.

    Let time taken by pipe B to fill the tank alone = x hrs.

    time taken by pipe A to fill the tank alone = ( x - 10) hrs.

    Part of the tank filled by pipe B in 1 hr. = 1/x

    Part of the tank filled by pipe A in 1 hr. = 1/(x - 10)

    Since the tank can be filled by A and B together in 12 hrs., so in 1 hr., 1/12 of the tank is filled. That is

    1/x + 1/(x - 10) = 1/12

    12(x - 10) + 12x = x(x - 10)

    12x - 120 + 12x = x^2 - 10x

    x^2 - 34x + 120 = 0

    (x - 30)(x + 4) = 0

    x = - 4 (rej.) or 30 hrs.

    118.

    Let time required by Stephy to complete the task alone = x days.

    Time required by Miki to complete the task alone = (x + 5) days.

    Time required for them to work together = (x - 4) days.

    In 1 day, Stephy alone can complete 1/x of the work

    In 1 day, Miki alone can complete 1/(x + 5) of the work.

    In 1 day, working together can complete 1/(x - 4) of the work.

    Therefore,

    1/x + 1/(x + 5) = 1/(x - 4)

    (x + 5)(x - 4) + x(x - 4) = x(x + 5)

    x^2 + x - 20 + x^2 - 4x = x^2 + 5x

    x^2 - 8x - 20 = 0

    ( x - 10)(x + 2) = 0

    x = - 2 (rej.) or 10 days.

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