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Math Help - Need urgent Help

  1. #1
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    Exclamation Need urgent Help

    There are three pipes connecting a large water tank to a pool. Each of the pipes fills the pool at a uniform rate but the rates of different pipes are different. To fill the empty pool, one can open the first pipe for 2 hours and then the second pipe for 1 hour. Also using the second pipe for 2 hours and the third pipe for 1 hour fills the empty pool. If the pool is empty and the first pipe was open for 80 minutes, then the second pipe was open for 80 minutes, for how long does the third pipe need to be open after that to fill the pool?

    Plz help quickly - this is due 2moro!!!
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  2. #2
    Junior Member hoeltgman's Avatar
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    The main problem here is to put the text into equations. So let's do that first.
    We'll call:
    x= first pipe water
    y= second pipe water
    z= third pipe water
    In order to avoid any discussion with 0 divisions, we suppose that the amount water we get from the pipes is different from 0.

    For the pool I suppose that it is empty when the result of an equation is 0. If it's full, it's 1.

    In that case we get:

    2x+y=1 (1)
    2y+z=1 (2)
    4/3x+4/3y+az=1 (3)

    a is the time in hours we need to fill up the pool with the third pipe.

    From now on, it should be easy:
    (1) --> y=1-2x
    (2) --> z=1-2y
    Put into (3):
    you will get x=1/4 (you will eventually need to substitute an y with (1).)
    this helps us to find y in (2): y=1/2

    Put these two results in (3) again and you get a=0. You actually don't need the third pipe anymore
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  3. #3
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    Smile Thanks

    Thankyou for your help.
    Much appreciated
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  4. #4
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    Thumbs down

    Quote Originally Posted by hoeltgman
    The main problem here is to put the text into equations. So let's do that first.
    We'll call:
    x= first pipe water
    y= second pipe water
    z= third pipe water
    In order to avoid any discussion with 0 divisions, we suppose that the amount water we get from the pipes is different from 0.

    For the pool I suppose that it is empty when the result of an equation is 0. If it's full, it's 1.

    In that case we get:

    2x+y=1 (1)
    2y+z=1 (2)
    4/3x+4/3y+az=1 (3)

    a is the time in hours we need to fill up the pool with the third pipe.

    From now on, it should be easy:
    (1) --> y=1-2x
    (2) --> z=1-2y
    Put into (3):
    you will get x=1/4 (you will eventually need to substitute an y with (1).)
    this helps us to find y in (2): y=1/2

    Put these two results in (3) again and you get a=0. You actually don't need the third pipe anymore

    THIS is wrong!!!

    to solve -

    2x + y +
    2x + y +
    2y + z

    = 4x + 4y + z

    change to minutes

    = 320x + 320y + 60z
    \3
    = 80x + 80y + 20z

    Therefore the answer is 20 minutes of z!!!
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  5. #5
    Junior Member hoeltgman's Avatar
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    Sorry I wasn't entirely sure about this...
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  6. #6
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    Don't worry

    Its cool

    I had time to change it.

    But thanks anyway 4 your time.
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  7. #7
    MHF Contributor
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    Here is one way.

    Let
    x = rate of 1st pipe
    y = rate of 2nd pipe
    z = rate of 3rd pipe
    V = total volume of the pool

    ---------
    "To fill the empty pool, one can open the first pipe for 2 hours and then the second pipe for 1 hour."

    volume = rate * time

    V = x(2.0) +y(1.0)
    V = 2x +y ------------(1)

    --------
    "Also using the second pipe for 2 hours and the third pipe for 1 hour fills the empty pool."

    V = y(2.0) +z(1.0)
    V = 2y +z ----------(2)

    ----------
    "If the pool is empty and the first pipe was open for 80 minutes, then the second pipe was open for 80 minutes, for how long does the third pipe need to be open after that to fill the pool?"

    I understand here that the 1st and 2nd pipes were closed after their 80-minute run each, and then the 3rd pipe was opened to finish filling the pool alone. So,

    x(80/60) +y(80/60) +z(t) = V
    (4/3)(x+y) +tz = V ------------(3)

    ---------------
    Too many unknowns (x,y,z,t,V) and only 3 independent equations! Zeez.

    Anyway, we are looking for t, in hours, so we try to eliminate the x,y,z,and V.

    We eliminate V.
    V from (1) = v from (2),
    2x +y = 2y +z
    2x +y -2y = z
    2x -y = z -----------(4)

    Substitute that into (3),
    (4/3)(x+y) +t(2x -y) = V ----------(5)

    Substitute the V from (1) into (5)
    (4/3)(x+y) +t(2x -y) = 2x +y
    Isolate t,
    t(2x -y) = 2x +y -(4/3)(x+y)
    Clear the fraction, multiply both sides by 3,
    3t(2x -y) = 6x +3y -4(x+y)
    3t(2x -y) = 6x +3y -4x -4y
    3t(2x -y) = 2x -y
    Divide both sides by (2x -y),
    3t = 1
    t = 1/3 hour -----****
    In minutes, t = (1/3)(60) = 20 minutes.

    Therefore, the 3rd pipe needs to be opened for 20 minutes to finish the job. ---answer.
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  8. #8
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    Talking Wow

    Thanks for the input ticbol,
    and hoeltgman.

    I really appreciate your help.
    Thanks again,

    War_lord man
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