Atank 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:

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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step-by-step explanation: