The "on the morrow" refers to the next day after receiving the command from the Lord to depart. Their departure that quickly after receiving the command gives a context to the information in this verse about collecting the needed provisions. Regardless of the number of people involved in the enterprise, the family could not have gathered sufficient provisions for the entire journey in a single day. They certainly would have added to their stores with fresh food, but they would clearly have been collecting provisions for some time.
When they enter the ship they bring "whatsoever thing we had brought with us, every one according to his age." It appears that each person was allotted an amount to bring with them, and that the quantity varied with age. This would be logical as age would in some way dictate necessity. Younger children would need less, parents more (for themselves and the needs of children).