# STEP problem: constructing differential equations to describe fluid mixing.

#### Jamesmaths

##### New member
Hi,

I'm wondering if someone could help me with problem 9 on the following paper:

Firstly, it seems there's a mistake, and the question should have V'(t) rather than V(t) as the subject of the given differential equation?

For the second part, someone on another forum has proposed a solution in which the governing equation for the amount of chemical A in the second vat at a time t is V'(t) = (bV)/K - (cV)/L where, as I understand it, (V/K) in the first term describes the proportion of chemical A in the first vat, and (V/L) uses V to describe the proportion of chemical A in the second vat. It seems to me that V is being used in two different contexts here, invalidly, and that the expression already derived for the amount of chemical A leaving the first vat should be used to describe the amount of chemical A entering the second vat?

Help would be greatly appreciated.

James

#### HallsofIvy

##### Elite Member
It does. Although it is hard to see, there is a "dot" above the V which is yet another way of writing the derivative of V.

#### ronaledsmith

##### New member
Also finding the way to solve this from last week.