A tank contains $100 gal$ of pure water initially. From t=0, a brine contains 4lb of salt per gallon flows into the tank at a rate of $5\frac{gal}{min}$. The mixture is kept uniform by stirring and the outflow of the liquid is slower that is $3\frac{gal}{min}$.
When there is $50 lb$ of salt in the tank
My attempt is:
$$\frac{dx}{dt}=20-\frac{3x}{100+2t}$$
Solving it we have
$$x(100+2t)^{\frac{3}{2}}+4(100)^{\frac{5}{2}}=4(100+2t)^{\frac{5}{2}}$$
What I got is $2.59$ minutes but the book suggests $2.72$ minutes. I have tried but it seems not possible for me