Three Hobbits named Gordo, Prodo, and Mongo are harvesting a field of carrots. The carrot field is 20 meters wide by 40 meters long. Mongo worked hard all summer irrigating the field from a nearby creek. 

Prodo harvests the field at a rate of 100 square centimeters per minute.
Gordo harvests the field at a rate of 200 square centimeters per minute.
Mongo harvests the field at a rate of 400 square centimeters per minute. Mongo feels like he doesn't need to harvest because of the amount of work he put in throughout the summer.

Three hours into harvesting the carrots, Prodo and Gordo convince Mongo to help. The amazing work ethic of Mongo improves the productivity of Prodo and Gordo to 300 square centimeters per minute each.

How long, in minutes, does it take Prodo, Gordo, and Mongo to harvest the entire carrot field?