I"m not sure how that is figured. But it is more about the draw of the engine and duration of the ride. The question is how big an engine would you need. Then you would need to figure it's amp draw and buy a battery with enough amps to supply it.
For instance I ran an 80cc kit engine for a while. I also ran a lot of DIY friction drive weed eaters. Now I run a 250Watt hub motor and a friction drive 300watt motor.
The 250 watt hub motor is slightly more powerful, not a lot, but slightly. It is 24volt. I am just now testing the range of the batteries on it. The 250 watt has about the same power as a 20cc or so friction drive.
The battery duration on 12ah sealed lead acid batteries was about 4.25miles with me helping by pedaling with the engine most of the time. I tested it today with very little pedal assist and got almost the same results. It went to dying power about a quarter mile sooner but I still got it home.
So what you need is not just a battery pack with the power for that short burst of high amps, but one with enough stored power to get you where you are going as well.
Right now you can buy a 1000watt 48volt system. I would think that would pull that hill with some help. If it works like my system, which I doubt that it would, I would guess maybe five miles on a 12ah battery pack.
They say twenty on their packs. My guess is they are talking 20ah batteries which might get you under ten miles in the real world. On a flat course with no hills or stops you could probably get close to their advertised distances.
I have to finish my tests to be definitive, so I can't really answer your question with any degree of confidence. All this is mostly conjecture.
I also plan to build a chain driven e bike which might be totally different.
Weight depends on the battery type. the SLA is the cheapest and the heaviest. I will be using them because I can't afford the more expensive ones. If money were no object, I would buy the Nichol hydride battery pack.
The sla 20amp hour four pack would probably run you close to $200 as a guess on ebay. I bought a two pack of 12ah and they were around fifty dollars.
There are others who know much more about this than me. So wait for more input before you make any decisions.
ps. A 12ah battery might put out one amp for 12 hours, which is the basis of the rating, but it sure as heck wont put out 24amps for half an hour. You would think that it would, but it won't come close.