ABC Company is unloading coal from a barge on the Mississippi River. The barge contains 1,760 tons of coal. The coal is shoveled out of the barge with a material handling machine into dump trucks. Each truck takes 4 minutes to load, 4 minutes to travel to the dump site, 4 minutes to dump, and 4 minutes to return. Each dump truck holds 22 tons of coal. Assuming no delays, how quickly can the barge be unloaded and what is the optimal number of dump trucks to be used?

The answer is: 5 hours 20 minutes; 4 Trucks

Explanation:

Each truck has a 16 minute window to pick up and dump the coal. This process can be observed as an assembly line where each stage of production is the stages of coal transport. When Truck A is travelling to the dump site, Truck B can be loading the coal. When Truck B is travelling to the dump site and Truck A is dumping the coal, Truck C would be loading the coal. When Truck A is travelling to the loading area, Truck B dumping the coal and Truck C travelling to the dump site, Truck D would be loading the coal. Once Truck A gets to the loading area, Truck D would be on its way to the dump site and so on. In each 16 minute window 88 tons of coal (22 tons * 4) is picked up and dumped, that is, 22 tons every 4 minutes. Given that there are 1, 760 tons of coal, the total time taken to dump all the coal is equal to 320 minutes:

88 tons = 16 minutes (22 tons dumped every 4 minutes)

1, 760 tons = (1760 tons * 16)/88 tons = 320 minutes

320 minutes/ 60 minutes = 5 hours 20 minutes

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