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Math Help - Volume of two tanks

  1. #1
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    Volume of two tanks

    Having problems with this volume question.

    There were 68000cm3 of water in tank X and tank Y. The heights of the water in both tanks are equal. Tank Y was 40% full of water. When all the water from tank Y was poured into tank X, 4litres of water overflowed.

    A) find the height of the water in tank X at first?
    B) find the capacity of tank Y?

    Thanks in advance
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  2. #2
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    Hello, spaarky!

    A challenging problem . . . I haven't solved it yet.


    \text{There are 68 liters of water in tank }X\text{ and tank }Y.
    \text{The heights of the water in both tanks are equal.}
    \text{Tank }Y\text{ is 40\% full of water.}
    \text{When the water from tank }Y\text{ is poured into tank }X,
    . . \text{4 liters overflowed.}

    \text{(A) Find the height of the water in tank }X\text{ at first.}
    \text{(B) Find the capacity of tank }Y.

    This how I envision the two tanks and the water.


    Code:
            Tank X         Tank Y
    
          *       *
          |       |
          |       |     *           *
          |       |     |           |
          * - - - *     * - - - - - *
          |:::::::|     |:::::::::::|
         h|:::A:::|    h|:::::B:::::|
          |:::::::|     |:::::::::::|
          *-------*     *-----------*

    There are A liters of water in tank X.

    There are B liters of water in tank Y.

    We know that: . A + B \:=\:68

    We see that: . A+B \,=\,68 is 4 more than the capacity of tank X.

    . . Hence, the capacity of tank X is 64 liters.


    We know that \,B is 40% of the capacity of tank Y.


    I need at least one more equation . . . Where is it?

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  3. #3
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    Exactly .... It's like on the tip of my tongue ... but no matter what I have written down so far doesn't quite get there.

    Base Area (BA)
    We also know the Ratio of BAa : BAb is the same as the Ratio of the Volume A : B.

    Also, for Capacity
    X : Y
    64 : B / .4
    160 : B
    So Y --> 160/B x X
    Y --> 10240/B

    And I think there is a mistake in here somewhere

    Also,
    The Base Area doesn't change so with a common Height,
    64 : 2.5B is also the the same as BAa : BAb --> A : B

    A : B --> 64 : 2.5B
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  4. #4
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    i view this as two rectangular tanks with the same base areas.Tank y has a capacity of 170 liters and tank x 132liters.Tank y is simply taller


    bjh
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  5. #5
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    I don't believe this is feasible.

    If the capacity of X : Y is 132 : 170

    Then, the original volume of water in Y would be 170 x 40% = 68

    This is the full amount of combined water. Thus the Height of the water in both Tanks, originally, would not be the same as indicated in the question.
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