How can I determine the activation energy of a reaction if the reaction rate constant is unknown?

I am trying to conduct an experiment to determine the activation energy of the following chemical reaction: 


1. $$\ce{IO3- (aq) + 3HSO3- (aq) -> I- (aq) + 3SO4^2- (aq) + 3H+ (aq)}$$
2. $$\ce{5I- (aq) + 6H+ (aq) + IO3- (aq) -> 3I2 (aq) + 3H2O (l)}$$


The Arrhenius Equation can be rewritten as $$\ln k = \frac{-Ea}{{\rm R}T} + \ln A$$ Therefore, if ln k and 1/T were plotted on a graph, the slope of the line should be equal to -Ea/R. 


I can use temperature as my independent variable and the reaction time as my dependent variable. However, I am unsure as to how to determine the reaction rate constant (k) of the reaction experimentally from the reaction time.


