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Math Help - Direct Variation

  1. #1
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    Direct Variation

    Having operated for 40 minutes, a small pump removed 30 gallons of water from a 8000-gallon swimmingpool. There is a linear relationship between the gallons of water V remaining n the pool and the pumping time t in minutes. Find the equation for this relationship.

    Can I be really dense and say eh?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by askmemath
    Having operated for 40 minutes, a small pump removed 30 gallons of water from a 8000-gallon swimmingpool. There is a linear relationship between the gallons of water V remaining n the pool and the pumping time t in minutes. Find the equation for this relationship.

    Can I be really dense and say eh?
    A linear relationship between V and t will take the general form: V=at+b where a and b are constants. You've actually got TWO data points, not one, if you read the question correctly, so you can find a and b.

    -Dan

    BTW: You weren't so dense as to not ask, so I wouldn't worry about it!
    Last edited by topsquark; February 24th 2006 at 11:36 AM. Reason: Addition to text
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  3. #3
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    Thans Dan for that re-assuring thought.

    Now let me plunge myself into deeper gloom by saying I have absolutely no idea what you are trying to hint at !!


    Waaahhh!!
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by askmemath
    Thans Dan for that re-assuring thought.

    Now let me plunge myself into deeper gloom by saying I have absolutely no idea what you are trying to hint at !!


    Waaahhh!!
    Let's just say I'm a bad hinter. Okay. The general definition of a linear relationship is one that is first power in the independent variable, ie. it is always of the form: y=ax+b. This is a line, and thus if we have two points on this line, we can find the slope a and intercept b.

    What information do we have in the problem. Obviously we know that it has taken us t = 40 min to pump 30 gal, so V= 8000 - 30 = 7970 gal. What other point on the line do we have? Well, how much water is "left" in the pool before we start pumping? In other words, when t = 0 min, V = 8000 gal.

    So: V = at + b, and we have the points (t,V) = (0, 8000) and (40, 7970). So now you can find a and b by plugging these two points into the equation and solve the two equations for the two unknowns.

    -Dan
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  5. #5
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    OK Thumbs Up Dan! That definitely made a whole lot more sense to me!
    Thanks a lot!!

    p.s. Isnt there some sorta way we can show our appreciation for these people by giving them points voted by us? for e.g. every answer can have an option of being voted upon by the original question poser.

    The higher the points, the cooler the dude!!
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  6. #6
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    Quote Originally Posted by askmemath
    Having operated for 40 minutes, a small pump removed 30 gallons of water from a 8000-gallon swimmingpool. There is a linear relationship between the gallons of water V remaining n the pool and the pumping time t in minutes. Find the equation for this relationship.

    Can I be really dense and say eh?
    One way of doing this is by "reasoning". :-)

    v = remaining volume of water in the pool
    So, after time t in minutes,
    v = 8000 -r*t ---------***
    where
    r = rate of pumping out the water, in gal/min.

    What is r?
    Given: 30gal in 40min.
    So, r = (30gal)/(40min) = 3/4 = 0.75 gal/min ---------***

    Therefore,
    v = 8000 -0.75t --------------answer.
    Last edited by ticbol; February 24th 2006 at 12:23 PM. Reason: where is "by"?
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  7. #7
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    For what its worth,Ticbol you get my vote as well

    Thank you so much
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