Final answer:
A person with a bush-hog cuts at a rate of 1.75 acres per hour. With a 30-hour work week, they cut 52.5 acres each week. It will take approximately 3.2 weeks to cut 168 acres.
Step-by-step explanation:
To calculate how many weeks it will take the person to cut 168 acres of brush with a bush-hog, we first find out how many acres can be cut in one hour and then use that rate to determine the total time needed.
The question states that 1 person can cut 10.5 acres in 6 hours. Therefore, the hourly cutting rate is:
Hourly rate = Total acres cut / Hours worked = 10.5 acres / 6 hours = 1.75 acres/hour
With a 30-hour work week:
Acres cut per week = Hourly rate × Hours per week = 1.75 acres/hour × 30 hours/week = 52.5 acres/week
The total weeks needed to cut 168 acres is:
Total weeks = Total acres to cut / Acres cut per week = 168 acres / 52.5 acres/week
After calculating the above expression, we find that:
Total weeks ≈ 3.2 weeks
Therefore, it will take approximately 3.2 weeks for the person to cut 168 acres of brush.