If it is a 10 watt panel and if it really does put out 10 watts when aimed perfectly at the sun on a cloudless day, your 19.2 amp hour battery pack is probably in the 60 to 70 watt hour range. Thus, perfect conditions, 6 to 7 hours.

My bike tour six years ago, my dynohub was not keeping my battery up like it should. Ended up plugging a charger into an outlet in a laundry room at a campground and found that my charger was not charging as fast is it should. At that point I started checking cables and found that I had a bum cable, half my power from the dynohub did not make it thru that cable. Changed cables, and I was self reliant for power with my dynohub for the rest of my tour.

Lesson learned, use good cables.

I also carry a meter so I can see how much power is going through my USB port, but if you don't know what the numbers mean, a good meter might not be of any help. In my case, the meter was how I discovered a bum cable was my problem, changed cables and the charger plugged into the outlet started putting twice the power into my battery pack.