(Note I am the OP)

**Master equation**

The master equation can be written as: 
$$\frac{d p_n(t)}{dt}=\sum_{n'}\{W_{nn'}p_{n'}(t)-W_{n'n}p_n(t)\}$$
Where $p_n$ denotes the probability that the system is in state $n$ at time $t$. And $W_{nn'}\Delta t$ denotes the probability of the system changing from state $n'$ to the state $n$ in the time interval $\Delta t$.

**Specific case**

Let us say we have $n=1$ free enzyme, then:
$$ \frac{dp_0(t)}{dt}=W_{01}p_1(t)$$
So what is $W_{01}$ this is the probability that the one enzyme is used up, let us call this $\mu$. 
$$\frac{dp_0(t)}{dt}=\mu p_1(t)$$
The average number of 'free enzymes' is given by: 
$$<n>=p_1(t)$$
Differentiating this gives:
$$\frac{d<n>}{dt}=\frac{dp_1(t)}{dt}$$
But in our case,
$$ \frac{dp_1(t)}{dt}=-\mu p_1(t)$$
Thus
$$\frac{d<n>}{dt}=-\mu p_1(t)$$
$$\frac{d<n>}{dt}=-\mu<n>$$
From here with the assumption that $\mu\propto [S]$ you can follow through my derivation on [Biology.SE][1]

**Sources**

1.'Stochastic processes in physics and chemistry' by N.G. Van Kampen chapter V

2.  http://www.jpoffline.com/physics_docs/y4s7/advstatmech_ln.pdf

  [1]: http://biology.stackexchange.com/questions/38576/dwell-time-equations-for-atp-sythase?noredirect=1