Final answer:
The longest time a food handler can safely take to cool food from 135°F to 41°F is 6 hours, with the process occurring in two stages.
Step-by-step explanation:
The longest amount of time a food handler can take to cool food from 135°F (57°C) to 41°F (5°C) and have it remain safe is 6 hours. More specifically, the food must be cooled from 135°F to 70°F (21°C) within two hours and then from 70°F to 41°F (5°C) within an additional four hours, totaling six hours.
This is because bacteria tend to multiply rapidly at temperatures between 40°F (4°C) and 140°F (60°C), what is known as the danger zone. Perishable foods left in the danger zone for more than two hours can become unsafe due to rapid bacterial growth.