Drop the speed requirement to 15mph or so, allow a little over an hour for the journey and have a charger at both ends and it's possible with any number of off the shelf bikes and kits.
But, a recumbent or racing bike ridden by somebody who's fit and prepared to put the effort in (with a shower at work!) could do this. So although we're now getting illegal for e-bikes adding some assist to that ought to be possible. The problem is that I don't know of anything off the shelf that really works well for those. You're into not just a home build, but perhaps home construction as well. There are people out there home brewing RC friction drives, RC chain drives, seriously over-amping controllers and hub motors that kind of get you there at the cost of unreliability and lots of work.
See the thread about Zero motorcycles as well. At a price, pure electric scooters and motorcycles are just beginning to appear with just enough range to meet your requirements. If it was me, I'd just get a second hand Burgman 400, customise it a bit and use that. And give up on trying to do it electric for a few years.
I'd like though to explore more a couple of E-Bike options.
1) A racing bike with a small, light, low power assist. Something like a small Bafang or Tongxin hub with a small wheel motor wind in a large rim, 48v ecrazyman controller and a custom Ping battery. The aim being to get some assist up to 30mph or so and enough power to help you up the hills even though it won't just zoom up on it's own. And with the overall bike still light enough that it's seriously fast with no assist.
2) A recumbent with some aerodynamics and more power. In the right 'bent weight should be less of a problem so there's more potential for speed and hill climbing ability. Improving the aerodynamics should seriously help efficiency in the 20-30mph range.
Neither of those will be especially cheap, you'll have to hunt down suppliers but they are perhaps do-able with the current state of the art.