48v 15 ah is perfect for 20-25 mph and 20 mile range. At 25 mph, you will get about 22 miles. At 20 mph you will get about 28-30 miles. That's on a bike with bad aero, like with some panniers.
48v 20 ah, crosses the line on being easy to carry. Definitely too much to put on top of a rear rack. If you have 48v 15 ah, it's too much to put on the rear rack of a bike with a rear motor and have it ride well.
The easy solution is to get a 48v 15 ah size battery, or ride a lot slower with a 12 ah. Carry it in the middle of the bike, and it will handle good. Ideal bikes are hardtail mtb's, comfort bikes, and beach crusiers. Look for large space in the triangle to mount the battery there. Often the largest space is found on the less expensive steel mtb's and cruisers. If cruiser, get one with a 7 speed rear gear, and v brakes. Only about $150 for those, so the bike need not cost an arm and a leg. I'm not sure which K2 bike you have, or if it's even got a frame with a triangle. It can be an option to use a front hub with a Y frame full suspension bike. I did that for 10,000 miles of commuting. The front motor allowed me to carry 15 ah on a rack. But mounting a front hub on a suspension fork is extremely tricky. Getting it wrong can cost you your teeth.
Then the rest is easy, any 48v rear hubmotor kit with 800-1000w will get you the power and speed you need to make the ride.
Efficiency is directly tied to speed, assuming you are comparing regular upright bikes like mtbs or cruisers. 20 mph takes 400-600w, 25 takes 600-800, 30 mph takes at least 1000w. 20-30 watthours per mile is typical for 20-25 mph travel. More if it's windy though. You have to slow down a lot to make the same range in headwinds.
Another option is two batteries. Particularly if you will really ride about 20 mph. Then 36v will be perfect, and two 10 ah 36v batteries is the perfect size. Same watthours as a 48v 15 ah. I found a 36v 20 ah pingbattery lifepo4 worked great for about 7000 miles of that commuting I did. It would fit in the triangle of a large frame mtb too.