Question

A tank contains 1000L of brine with 10kg of dissolved salt. Pure water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes?

Answer 1

(a) 5000 kilos

Explanation:

If is the amount of salt (in kg) after minutes, then and the total amount of liquid in the tank remains constant at 1000 L.

and

Because , we have

so

Since is continuous, , and the right-hand side is never zero, we deduce that is always positive.

Thus, and

(b)

After one hour,

Answer 2

its 5000kg

Explanation: