A 200 gallon tank is half full.

Thus,  gallon.

At time , tank contains  pounds of concentrate per gallon.

Concentrate per gallon enters into the tank  gallons per minute.

The solution mixture is withdrawn at  gallons per minute.

(a)

Volume of the solution at any time  is given by .

Find the time when tank be full, .

Tank is full in  .

(b)

.

Substitute corresponding values in the above expression.

Write the differential equation in the standard from .

Here  and .

Solution of first order linear differential equation  is .

Where integrating factor .

Find integrating factor.

Integrating factor .

Solution of the differential equation is

.

Find the constant by applying initial conditions.

At time , amount of concentrate in the solution .

Particular solution is .

Tank is full at .

.

At the time of tank is full, pounds of concentrate is . 

(c)

Volume of the solution at any time  is given by .

Find the time when tank be full, .

Tank is full in .

Consider .

Here .

Integrating factor .

Here  and .

Solution of the differential equation is

Find the constant by applying initial conditions.

At time , amount of concentrate in the solution .

Particular solution is .

Tank is full at  mins.

.

(a) .

(b) .

(c) .