168 men finish a work in 14 days. How many days will 56 men take to finish the same work?

To solve this problem, we can use the concept of "man-days." Man-days is a way to calculate the total amount of work done, which is the product of the number of workers and the number of days they work.

1. **Calculate the total work in man-days:**

\[
\text{Total Work} = \text{Number of men} \times \text{Number of days}
\]

For 168 men working for 14 days:

\[
\text{Total Work} = 168 \times 14 = 2352 \text{ man-days}
\]

2. **Find the number of days 56 men will take:**

Let \( x \) be the number of days 56 men will take to complete the same work.

\[
\text{Total Work} = \text{Number of men} \times \text{Number of days}
\]

Substitute the values:

\[
2352 = 56 \times x
\]

Solving for \( x \):

\[
x = \frac{2352}{56} = 42 \text{ days}
\]

So, 56 men will take **42 days** to finish the same work.

Would you like further details or have any other questions?

### Related Questions:
1. If 56 men can finish the work in 42 days, how many days will 28 men take?
2. If the number of men is doubled, how many days will it take to finish the work?
3. How many men are required to finish the work in 7 days?
4. If the number of men is reduced to half, how many days will they take?
5. How many men are needed to finish the work in 21 days?

### Tip:
In problems involving work, the total work done can be expressed as the product of the number of workers and the time taken. This helps in comparing different scenarios efficiently.

Learn how to solve a work and time problem where 168 men complete a task in 14 days. Using man-days calculation, find out how many days 56 men will take to finish the same work. Suitable for students in Grades 6-8.

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