Alex,
You battery will be fine for that journey.
24V x 3.7Ah = 89Wh available from the battery.
@ 60% system efficiency = 53.4Wh
So, for instance, that's about 200 Watts power available for a 15 minute journey (12 mph for 3 miles).
On the flat, without headwind, you will need something like 55 Watts to maintain 12mph.
On a 5% gradient, you will need approximately 300 Watts to maintain 12 mph.
Travelling at 20mph on the flat will take about 200 Watts.