Two substances $\ce{A}$ and $\ce{B}$ react with each other in such a way that $\ce{A}$ is $50\,\%$ consumed in $\pu{33 min}$ and $75\,\%$ consumed in $\pu{66 min}.$ Changing the concentration of $\ce{B}$ has no effect on the results. Which statement is true?
And the answer is:
This reaction is first order in $\ce{A}$ and zero-order in $\ce{B}.$
I understand why $\ce{A}$ is first order but I don't get why $\ce{B}$ is zero order. The equation for the half-life of a zero order reactant is $$t_{1/2} = \frac{[\ce{B}]_0}{2k}.$$
Doesn't this mean that the concentration for a zero-order reactant would affect the half-life?