Final answer:
John Smith was absent from Jamestown during the Starving Time due to an injury that required him to return to England for treatment before the harsh winter of 1609-1610 set in.
Step-by-step explanation:
John Smith was not in Jamestown during the Starving Time because, despite his efforts to secure resources and implement measures for survival, he faced setbacks. Smith had managed to secure supplies and had made significant changes for the colony's survival, such as insisting that all colonists work and improving housing and security. However, the food stores he had gathered were destroyed by rats, and after dealing with these crises, Smith was eventually injured by a gunpowder explosion and had to return to England for treatment before the winter of 1609-1610, which became known as the Starving Time.