Question

Two tanks each hold 3 liters of salt water and are connected by 2 pipes; the salt in each tank is kept well stirred. Pure water flows into tank A at a rate of 5 liters per minute and the salt water exits tank B at the same rate. Salt water flows from tank A to tank B at the rate of 9 liters per minute and it flows from tank B to tank A at a rate of 4 liters per minute. If tank A initially contains 1 kilogram of salt and tank B contains no salt, then set up the system of differential equations that govern the mass of salt in each tank t >= 0 minutes later.

Answer 1

@hartnn would you know how to solve this?

Answer 2

@calculusfunctions would you know how to solve this?

Answer 3

I'm helping someone else at the moment @zordoloom

Answer 4

okay

Answer 5

Let A represent the amount of salt present in tank A and B represent the amount of salt present in tank B after the process begins. Then ΔA and ΔB represent the change in the amount of salt in the tank during a short time interval Δt.

In order to write differential equations, you must explain what is happening instantaneously. In other words, we need to determine what changes will occur over a very short time interval Δt. Now

ΔA = (salt in) - (salt out) for tank A and similarly ΔB = (salt in) - (salt out) for tank . Where

(salt in) = (rate of water in) ⋅ Δt ⋅ (concentration of salt) Similarly

(salt out) = (rate of water out) ⋅ Δt ⋅ (concentration of salt)


@zodoloom Now you try it because as you know I'd rather teach than give out solutions.