I will not say that it cannot be done.
For 10 months in 2006 and 2007 I commuted by bike; 19 miles AM 9 miles PM
19 miles in the morning 90 minutes was the standard time.
Hereś how the first 3 months went. Monday and Tjesday I was fine. Wednesday I was tired. Thursday, exhausted. Friday took every bit of grit I could muster to get through the day. Weekends, I did not allow mywelft to do anything strenuous because I knew Monday it starts again.
I would say, based on my experience that if you can do the distance in your timeframe that your biggest issue will be exhaustion.
Give it a try. Let us know how it goes or went. Should be interesting.
fat biker
P.S. If you are originally from the planet krypton none of what I wrote applies.