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Math Help - Rational equation to solve mixture problem

  1. #1
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    Rational equation to solve mixture problem

    A pollutant has leaked into a water tank containing 2000 gallons of water. The tank now is 3% pollutant. How much clean water should be added to the tank to decrease the concentration of the pollutant to a safe level of 0.5%?

    TIA!
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  2. #2
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    Quote Originally Posted by eagertolearn View Post
    A pollutant has leaked into a water tank containing 2000 gallons of water. The tank now is 3% pollutant. How much clean water should be added to the tank to decrease the concentration of the pollutant to a safe level of 0.5%?

    TIA!
    Let the present volume of liquid present in the fluid be Vi.
    3% is pollutant.
    After adding fresh water, let the vol. of the tank be Vf and pollutant drops to 0.5%. Since the amount of pollutant remains same before and after adding water, we will take a material balance of the pollutant.

    therefore,
    (3/100)*Vi = (0.5/100)*Vf

    We need to know amount of clean water added, i.e. Vf-Vi

    Now, initially we had 2000 gallons of water. after addition of pollutant it becomes 97%.
    therefore, 97% of Vi = 2000 gallons.

    First solve for vVi, then Vf and finally Vf - Vi to get the answer.
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  3. #3
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    Hello eagertolearn
    Quote Originally Posted by eagertolearn View Post
    A pollutant has leaked into a water tank containing 2000 gallons of water. The tank now is 3% pollutant. How much clean water should be added to the tank to decrease the concentration of the pollutant to a safe level of 0.5%?

    TIA!
    Can I suggest an alternative method, using ratios?

    Initially, there are 2000 gallons of water in the tank, which is 97% of the total amount. The remaining 3% is pollutant. So the ratio of water to pollutant is 97:3. The amount of pollutant in the tank is therefore:
    \frac{3}{97}\times 2000= 61.856 gallons
    After adding extra water, this has to be 0.5% of the total, the other 99.5% being water. So now the ratio of water to pollutant is 99.5:0.5=199:1. Since there are still 61.856 gallons of pollutant in the tank, the amount of water must now be:
    61.856\times199 = 12309 gallons
    Therefore, we must add 12309 - 2000 = 10309 gallons of water.

    Grandad
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  4. #4
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    Thanks annran and grandad!
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