A farmer can plough a field working 3 hours per days in 9 days. The farmer has to work how many hours per days to finish the same work in 6 days?

Answer

To solve the problem step by step, we will use the relationship between the number of men, days, hours per day, and the work done.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The farmer works for 3 hours per day (h1 = 3).
- The farmer works for 9 days (d1 = 9).
- We need to find out how many hours per day (h2) the farmer needs to work to finish the same work in 6 days (d2 = 6).

2. **Calculate the Total Work Done in the First Scenario:**
- Total work (W) can be calculated as:
\[ W = m1 \times d1 \times h1 \]
- Here, m1 (number of men) is 1 (the farmer), so:
\[ W = 1 \times 9 \times 3 = 27 \text{ hours} \]

3. **Set Up the Equation for the Second Scenario:**
- In the second scenario, the total work done is the same (W = 27 hours).
- We can express this as:
\[ W = m2 \times d2 \times h2 \]
- Again, m2 is 1 (the same farmer), so:
\[ 27 = 1 \times 6 \times h2 \]

4. **Solve for h2:**
- Rearranging the equation gives:
\[ 27 = 6 \times h2 \]
- To find h2, divide both sides by 6:
\[ h2 = \frac{27}{6} = 4.5 \text{ hours} \]

5. **Conclusion:**
- The farmer needs to work **4.5 hours per day** to finish the same work in 6 days.