The first thing in all of these kinds of analyses is that you want to decide what your criteria for food going off is: is it a probability? Maybe the mean number of days for something to go off? Perhaps a rate at which the food goes off?
This is the first and most critical step in statistical analyses and this will help you decide how to form your hypotheses.
You say you want to check at what time the food goes bad but how do you quantify what bad is? Is it more than 50%? 75%? 90%?
Once you answer this, you will have actually solved half the problem since the rest is setting up the analyses, doing the computation and interpreting the results.