If it takes 6 men 8 hours to dig a hole, how many hours would it take 4 men working at same rate?

This problem involves inverse proportionality, meaning as the number of men decreases, the time taken to complete the same amount of work increases. The foundational principle is that the total amount of work (man-hours) remains constant. First, calculate the total work units: 6 men * 8 hours = 48 man-hours.

The correct answer is B: 12. To find out how many hours it would take 4 men, divide the total work by the new number of men: 48 man-hours / 4 men = 12 hours. This demonstrates the inverse relationship.

• A: 10 is incorrect. This would imply a direct relationship or a miscalculation.
• C: 14 is incorrect and lacks a logical basis within the problem's context.
• D: 16 is incorrect. This would suggest that fewer men take even longer than the correct inverse proportion, or it's a result of an incorrect calculation like 8 + (8/2).