Question

Initially 10 grams of salt are dissolved into 30 liters of water. Brine with concentration of salt 4 grams per liter is added at a rate of 6 liters per minute. The tank is well mixed and drained at 6 liters per minute.

A)Let x be the amount of salt, in grams, in the solution after t minutes have elapsed. Find a formula for the incremental change in the amount of salt, Δx, in terms of the amount of salt in the solution x and the incremental change in time Δt. Enter Δt as Deltat.

B)Find a formula for the amount of salt, in grams, after t minutes have elapsed.

Answer 1

I'm not so sure about the first part, but the for the second, you must solve the following differential equation:
\[x'=\left(4\frac{g}{L}\right)\left(6\frac{L}{min}\right)-\left(\frac{x}{30}\frac{g}{L}\right)\left(6\frac{L}{min}\right)\\
x'+\frac{1}{5}x=24\]
With the initial condition \(x(0)=\dfrac{10}{30}=\dfrac{1}{3}\).