Question

A tank contains 100L of water. A solution with a salt concentration of 0.7kg/L is added at a rate of 7L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 5L/min. Answer the following questions.
1. If y(t) is the amount of salt (in kilograms) after t minutes, what is the differential equation for which y is satisfied?
2. How much salt is in the tank after 50 minutes?

Answer 1

\[y'(t)=(\text{rate flowing in})(\text{concentration flowing in})-(\text{rate out})(\text{conc. out})\]
The given information tells us that the differential equation modeling this situation is
\[y'=4.9-\frac{5}{100+2t}y\]
If you don't understand the setup, do ask.

Answer 2

Thanks so much!

Answer 3

You're welcome!