How do I solve this AP Chemistry problem on biodiesel

Question

In an effort to become more environmentally friendly, you have decided that your next vehicle will run on biodiesel that you will produce yourself. You have researched how to make the biodiesel in your own home and decided your best bet is to use the following chemical reaction:

 

Oil+NaOH(in methanol)===>biodiesel + glycerin

 

You preformed a test reaction in your kitchen to study the kinetics of this process. You were able to monitor the concentration of the oil and found that the concentration dropped from 0.500M to 0.250M in 20.0 minutes. It took an additional 40.0 minutes for the concentration of the oil to further drop to 0.125M. How long will it take for you to convert 97.0% of the oil to biodiesel?

Answer 1

Disappearance of oil in the first 20 min when initial [oil] = 0.5M = 0.25 M/20 min = 0.0125 M/min

Disappearance of oil in the next 40 min when initial [oil] =0.25 M = 0.125/40 min = 0.003125 M/min

Doubling [ ] from 0.25 to 0.5 results in a 4 fold increase in rate, thus the reaction is 2nd order

For second order, the integrated rate equation is 1/[A] = 1/[A]_o + kt.

From rate = k[oil]², you can solve for k using any of the rates and corresponding [ ] in the given problem.  After finding k, substitute it in the integrated rate equation using [A]_o = 1 and [A] 0.03 and solve for t.