00:01
In this question, we're given the mixing tank problem.
00:04
We're told that at time t equals zero, a solution has v not gallons of liquid, and it has q0 pounds of concentrate in it.
00:12
We're told that there is q1, a solution with q1 pounds per gallon of concentrate that's being added to the solution at r1 gallons per minute.
00:22
We're told that the solution is mixed and it's emptied at a rate of r2 gallons per minute.
00:27
And we want to find the quantity of the concentrate, for all times.
00:35
In order to do this, we have to know that dq, dt, is equal to the rate in minus the rate out.
00:48
And it's basically the rate in or out is equal to the flow times the concentration.
01:01
Now for the rate in, we know that this is going to be q1 pounds per gallon, q1 pounds over r1, or times r1.
01:14
So we're going to suppose that it's going to be q1, r1, but r1 and r2, which are the in -rates and out -rates, are going to be the same...