Great.
All the numbers shown below are from this calculator http://bikecalculator.com/
It's very accurate in my experience. Relatively easy to use, so play with it if you want.
Assumptions:
200lbs = weight of rider and bike
14mph = average speed
No wind, no hill, smooth road.
80% efficiency for motor & controller.
Case #1: The motor does all the work (no assist from the rider)
Required power = 140W
Required power after motor/controller inefficiency = 140 / 0.8 = 175W
So 175Wh are needed to travel 14 miles at 14mph. Or 12.5Wh/mile.
Your battery has 480Wh, so your range will be 480/12.5 = 38.4 miles.
In the real world, there will always be some wind, some inclination on the road. So take away 10% to compensate for those. New range = 34.6 miles.
Most people don't want to use all the energy in the battery. They tend to recharge when the battery is about 90% depleted. So take away another 10%.
Final range = 31.1 miles.
Case #2: 50% assist from the rider.
You provide half the power or 70W. Normal adults usually do 100 to 150W, so 70W should be very easy.
Your range doubles to 62.2 miles.
BTW, it makes no difference whether your batteries are in parallel or in series. 14mph can be done with either voltage (24 or 48). The question is what voltage does the controller require.
Edit to add: Since you already ordered the motor and controller and they are apparently set for a 36V battery, that what you want to buy. A 36V 15Ah battery will give you 540Wh, slightly more (12%) than your two 24V batterier. Assuming of course that it would fit where you intend to. All the energy consumption rate calculations remain the same, except now you have a 12% longer range.
