Reaction kinetics, relating half life to reaction rate How do I relate the half life to the overall rate of reaction? 

I argued that from the data, doubling the partial pressure of either reactant, keeping the other constant, will half the half life. 

So try t1/2 = 
$\frac{\ce{[1]}}{\ce{[k][PA_0][PB_0]}}$ and since pressure of A is always greater than B, so t1/2 = $\frac{\ce{[1]}}{\ce{[k'][PB_0]}}$ ?

I then wrote:
$$\frac{-\mathrm{d}[PB]}{\mathrm{d}t} = k [P_B]^m $$, where k = k[PA]
Recall the meaning of the half life $t_{1/2}$: At $t_{1/2}$, a concentration (or partial pressure) is decreased to the half of its initial value.

It is crucial to realize that this represents exactly the $\mathbf{-\frac{dp_A}{dt}}$ in your rate equation!

With other words, $-\frac{dp_A}{dt} = k\cdot p_A\cdot p_B^2$ becomes $-\frac{54}{2\cdot100} = k\cdot54\cdot(1.0)^2$ for your first set of data. 

Solve for $k$ and do the same for the other data sets. What is the result?