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30 June, 19:47

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drains from the tank at the rate 7 L/min. Let y o u be the number of kg of salt in the tank after t minutes. The differential equation for this situation would be:

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  1. 30 June, 20:13
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    dy/dt = 7y / (t - 1000)

    Step-by-step explanation:

    Change in mass of salt = mass of salt going in - mass of salt going out

    dy/dt = 0 - (C kg/L * 7 L/min)

    where C is the concentration of salt in the tank.

    The concentration is mass divided by volume:

    C = y / V

    The volume in the tank as a function of time is:

    V = 1000 + 6t - 7t

    V = 1000 - t

    Therefore:

    C = y / (1000 - t)

    Substituting:

    dy/dt = - 7y / (1000 - t)

    dy/dt = 7y / (t - 1000)

    If we wanted, we could separate the variables and integrate. But the problem only asks that we find the differential equation, so here's the answer.
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