2) Google maps estimates that this distance would take 2 hours to complete.
Would it be possible (depending on the bike and fitness) to do this distance in about an hour?
Given that most commutes have a number stops, to ride 35 km in an hour you would be having to be averaging speeds around 40 kph+ when moving (likely more depending on the length of stops). This could be done by a very fit rider, on a TT bike every so often.
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To do this level of effort consistently 2-3 times every week, week after week, into head winds and rain, while carrying a load (e.g., lunch and cloths) is incredibly doubtful.
If you can't spare more time, one option could be some of the high performance pedalec bikes. Some of very high-end ones these can sustain speeds of 45 kph and have ranges up to 80-100km.
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A few of these also do a good job matching your input power the profile so that you do not notice the assist (you just feel faster). Because you still have to work with a pedalec, it is still possible to get a good workout by modifying the level of assistance.
One additional considerations are your local laws.
For example, in Canada I believe pedalecs are legally limited to 32 kph.
So a 45 kph pedelecs may be illegal unless registered as a moped! Although there may be legal loop holes with how the bike provides assistance (i.e., no throttle). I am no lawyer, so take this caveat with a grain of salt.