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    I'm having difficulty interpreting differential equations in essay form. Eg:

    A tank contains a solution of salt in water. Initially the tank contains 1000 l of water with 10 kg of salt dissolved in it. The mixture is poured off at a rate of 20 l per min, and simultaneously pure water is added at a rate of 20 l per min. All the time the tank is stirred to keep the mixture uniform. Find the mass of the salt in the tank after 5 mins. The tank must be topped up by adding more salt when the mass of the salt in the tank falls to 5 kg; after how many mins will it need topping up?

    Can someone please talk me through it?
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    (Original post by Zapsta)
    I'm having difficulty interpreting differential equations in essay form. Eg:

    A tank contains a solution of salt in water. Initially the tank contains 1000 l of water with 10 kg of salt dissolved in it. The mixture is poured off at a rate of 20 l per min, and simultaneously pure water is added at a rate of 20 l per min. All the time the tank is stirred to keep the mixture uniform. Find the mass of the salt in the tank after 5 mins. The tank must be topped up by adding more salt when the mass of the salt in the tank falls to 5 kg; after how many mins will it need topping up?

    Can someone please talk me through it?
    Sack that, I swear if that comes up in the exam I'm done for, I really dislike differential equations.
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    (Original post by Zapsta)
    I'm having difficulty interpreting differential equations in essay form. Eg:

    A tank contains a solution of salt in water. Initially the tank contains 1000 l of water with 10 kg of salt dissolved in it. The mixture is poured off at a rate of 20 l per min, and simultaneously pure water is added at a rate of 20 l per min. All the time the tank is stirred to keep the mixture uniform. Find the mass of the salt in the tank after 5 mins. The tank must be topped up by adding more salt when the mass of the salt in the tank falls to 5 kg; after how many mins will it need topping up?

    Can someone please talk me through it?
    This is probably too late but anyway. I think that the rate of decrease of the amount of salt is proportional to the amount of salt in the tank. So,

    dS/dt = -kS

    You can then solve this and use the initial conditions: when t=0, S=10 but also to find k we use the fact that after one minute the amount of salt should be 9.8 kg; that is, when t=1, S=9.8. I obtain the relation

    S = 10(0.98)^t

    Can anyone verify this?
 
 
 
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