davsco

It's a poorly phrased problem, You need extra information. For example: 
1. Does each germ split only once? 
2. Does the germ die after splitting? 
 
If 1 & 2 are true, only one split and dies, then the final total is all that matters, therefore you only save one phase and 59 minutes is the correct answer. 
If  only 1 is true, only one split and lives, then you have a cumulative total which means that after 59 minutes the second scenario is still 1 germ short  therefore the 60th minute is needed to fill (and overflow) the jar. 
If neither 1 or 2 are true, germs live and prior generations continue to multiply, the the time is exponentially less = 1+2+6+18 etc 
 
My son has the program and the answer they want is 59 minutes therefore, in their scenario, the germs split only once and die after splitting ... this is not borne out by their explanatory illustration which appears after the puzzle.