Final answer:
To find out how long it takes for the sorting machine to sort 8,640 tons of oranges, we determine its processing rate and then use that rate to calculate the time required. The machine processes oranges at a rate of 720 tons per minute, leading to a result of 12 minutes to sort 8,640 tons.
Step-by-step explanation:
The student wants to know how long it will take a sorting machine to sort 8,640 tons of oranges based on the information provided that the machine can process 36,000 tons in 50 minutes.
First, we calculate the rate at which the sorting machine processes oranges per minute by dividing the total amount of processed oranges by the time in minutes:
Rate = 36,000 tons / 50 minutes = 720 tons per minute
Then, we calculate the time it will take to process 8,640 tons of oranges using the rate:
Time = 8,640 tons / 720 tons per minute
Time = 12 minutes
Therefore, the machine will take 12 minutes to sort 8,640 tons of oranges.