Sure! Let's break down the solution step by step.
Step 1: Initial Calculation
We start by understanding the given scenario:
- Two men are working 8 hours a day.
- They take 4 days to cultivate 1 acre of land.
First, we need to calculate the total man-hours needed to cultivate 1 acre of land.
- Number of men = 2
- Hours per day = 8
- Days needed = 4
Total man-hours needed per acre:
[tex]\[ \text{Man-hours needed per acre} = 2 \text{ men} \times 8 \text{ hours/day} \times 4 \text{ days} = 64 \text{ man-hours} \][/tex]
Step 2: New Scenario Calculation
Now, let's consider the new scenario:
- Six men are working 4 hours a day.
- We need to find out how many days they will take to cultivate 4 acres of land.
First, calculate the total man-hours available per day:
- Number of men = 6
- Hours per day = 4
Total man-hours available per day:
[tex]\[ \text{Man-hours per day} = 6 \text{ men} \times 4 \text{ hours/day} = 24 \text{ man-hours/day} \][/tex]
Step 3: Calculate Total Man-Hours Needed for 4 Acres
We know from the initial calculation that it takes 64 man-hours to cultivate 1 acre. Therefore, for 4 acres:
[tex]\[ \text{Total man-hours needed} = 64 \text{ man-hours/acre} \times 4 \text{ acres} = 256 \text{ man-hours} \][/tex]
Step 4: Find the Number of Days Required
We need to find out how many days it will take for the six men working 4 hours a day to complete 256 man-hours of work. We already calculated that they can work 24 man-hours per day. Therefore:
[tex]\[ \text{Days required} = \frac{\text{Total man-hours needed}}{\text{Man-hours per day}} = \frac{256 \text{ man-hours}}{24 \text{ man-hours/day}} = 10.\overline{6} \text{ days} \][/tex]
So, it will take 6 men, each working 4 hours a day, approximately 10.67 days (or 10 days and 16 hours) to cultivate 4 acres of land.
