Eight men can dig a field 14 days,working 6 hours a day. In how many days can 7 men dig the same field, working 8 hours a day ?

Answer

To solve the problem, we need to determine how many days it will take for 7 men to dig the same field, working 8 hours a day, given that 8 men can dig the field in 14 days working 6 hours a day.

### Step-by-step solution:

1. **Calculate the total work done by 8 men in hours:**
- The total work done can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Hours per Day} \]
- For 8 men working for 14 days at 6 hours a day:
\[ \text{Total Work} = 8 \times 14 \times 6 \]

2. **Perform the multiplication:**
- First, calculate \( 8 \times 14 = 112 \).
- Then, multiply \( 112 \times 6 = 672 \).
- So, the total work done is 672 man-hours.

3. **Set up the equation for 7 men working 8 hours a day:**
- Let \( x \) be the number of days required for 7 men to complete the same work.
- The total work done by 7 men working 8 hours a day is:
\[ \text{Total Work} = 7 \times x \times 8 \]

4. **Equate the two expressions for total work:**
- Since both expressions represent the same total work, we can set them equal to each other:
\[ 672 = 7 \times x \times 8 \]

5. **Simplify the equation:**
- Calculate \( 7 \times 8 = 56 \):
\[ 672 = 56x \]

6. **Solve for \( x \):**
- Divide both sides by 56:
\[ x = \frac{672}{56} \]

7. **Perform the division:**
- Simplifying \( \frac{672}{56} \):
- First, divide both by 8:
\[ \frac{672 \div 8}{56 \div 8} = \frac{84}{7} = 12 \]
- Thus, \( x = 12 \).

### Conclusion:
- Therefore, it will take 7 men **12 days** to dig the same field while working 8 hours a day.