A fellow teacher!!! Absolutely something like that is feasible. Hub motors are pretty powerful these days. You could stick one of those in one or both front wheels. If you want it to move pretty well, I would do at least 36 volts, and at least 20 amps. Power is volts*amps, and you would probably need around 1 HP for 2 people, which is 746 watts. 36*20 = 720 watts. YOu could use a cheaper motor if you can get a gearing thing to work like with a belt or chain. Sealed Lead Acid batteries would probably be the easiest and cheapest way to go.
Two Sealed Lead Acid 12120 Rechargeable Scooter Batteries (2) - Nearly New | eBay
Lithium like "Headway" batteries would be better, but more expensive. Crap I have to go to school now to!