Question

A tank contains 60 kg of salt and 2000 L of water. A solution of a concentration 0.015 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.

Let y be the number of kg of salt in the tank after t minutes.

Write the differential equation for this situation

Answer 1

I suspect the equation is something like this:
\[
\frac{dy}{dt}=\underbrace{8\times0.015}_{\text{inflow of salt}}-\underbrace{8\times y}_{\text{outflow of salt}}
\]

Answer 2

I am extremely uncertain though.

Answer 3

Take it with a grain of salt ;)

Answer 4

@phi @rational

Answer 5

how many kg of salt flow in per min ?

Answer 6

how many kg of salt flow in per min ? 8 L / min * 0.015 kg/L = 0.12 kg/ min

next, how many kg of salt flow out ?
to answer, you first need to find how many kg/L of salt is in the vat (assuming it's nicely mixed). then multiply by 8 L/min

can you answer how many kg/L of salt is in the vat ?