Predicting rate equations from data I am having trouble wit the following question on my problem sheet:

"The reaction $\ce{Br- + ClO^- \to BrO^- + Cl^-}$ occurs with a rate constant of $\text{0.35 dm}^3 \text{mol}^{-1}
\text{s}^{-1}$

at
298 K. For the following initial conditions calculate the time taken for the Br^-
concentration to fall to half its original value:

i) $[\ce{Br-}]=[\ce{ClO-}]=0.0017$

ii) $[\ce{Br-}]=0.0017$ and $[\ce{ClO-}]=0.084$"

I am sure I could do this question if I knew the rate equation but it isn't given. From the units of the rate constant the reaction must be second order but how am I supposed to know whether it's second order with respect to one of the reactants (and thus zeroth order w.r.t the other) or first order with respect to both? Also, what's the significance of the concentrations being equal (there's another question that stresses that the concentrations of both the reactants are equal).
You have to assume it is first order in each reactant.

Zero-order kinetics is always an artifact of the conditions under which the reaction is carried out.

The reaction can't really be zero-order in a reactant, otherwise it would imply the reaction continues after there is no reactant remaining.