Final answer:
To find out how long it will take 10 farmers to churn 12 gallons of butter, we calculate the rate per farmer per hour and then use that rate to find the time for 10 farmers to churn 12 gallons. It will take 45 minutes, answer D.
Step-by-step explanation:
The subject of the question is mathematics, and it requires us to solve a problem involving rates of work. Specifically, this problem is a proportionality question that connects the number of workers to the amount of work done and the time it takes to complete.
First, let's find out how much butter one farmer can churn in one hour. Since 12 farmers churn 96 gallons in 5 hours, we can calculate the rate per farmer per hour by dividing the total amount of butter by the number of farmers and then by the number of hours:
Rate per farmer per hour = (96 gallons) / (12 farmers × 5 hours) = 1.6 gallons per farmer per hour.
Next, we need to find out how long it will take 10 farmers to churn 12 gallons of butter:
Time = Total gallons / (Rate per farmer per hour × Number of farmers)
Time = 12 gallons / (1.6 gallons per farmer per hour × 10 farmers) = 12 / 16 = 0.75 hours.
Since we want the time in minutes, we convert hours to minutes by multiplying by 60:
Time in minutes = 0.75 hours × 60 minutes per hour = 45 minutes.
Therefore, the correct answer is D) 45 minutes.