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To solve this question, let's break it down into parts.

### Step 1: Define the Rates of Work for Men and Women
Let's assume:
- The work rate of one man is \(M\).
- The work rate of one woman is \(W\).

According to the question, **6 men and 9 women can complete the work in 2 days**. Therefore, the combined work rate of 6 men and 9 women is enough to finish 1 unit of work in 2 days. We can express this as:
\[
2 \times (6M + 9W) = 1
\]
Simplifying:
\[
6M + 9W = \frac{1}{2}
\]

### Step 2: Find the Relationship Between Men’s and Women’s Rates
The question also states that **3 men take one day less than 4 women to complete the work**. This implies:
- If 4 women take \(d\) days to complete the work, then 3 men would take \(d - 1\) days.

Since the total work done is 1 unit, we have:
\[
4W \times d = 1
\]
and
\[
3M \times (d - 1) = 1
\]

From these, we can solve for \(d\) and find the individual rates \(M\) and \(W\).

### Step 3: Calculate the Time for One Man and One Woman to Complete the Work
Once we have the values of \(M\) and \(W\), we can determine how long it would take for one man and one woman to complete the work by finding:
\[
\frac{1}{M + W}
\]

Let me know if you'd like detailed calculations for each step or if you have specific questions about any part! 

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#### Related Questions
1. How would the solution change if the work rate for women was different?
2. What if the question specified different numbers of men and women completing the work in the initial conditions?
3. Can this problem be solved by setting up and solving a system of equations for \(M\) and \(W\)?
4. How does the work rate equation change if men and women work at different times?
5. What assumptions are we making about the uniformity of work rates in this problem?

#### Tip
In such problems, defining variables for unknown work rates and setting up equations based on total work is key to solving the question systematically.

6 men and 9 women can complete the work in 2 days. Three men take one day less than four women to complete the work. In how many days can one man and one woman complete the work?

Solve this time and work problem where 6 men and 9 women can complete a task in 2 days, and 3 men take one day less than 4 women to finish the task. Learn step-by-step how to calculate the time needed for one man and one woman to complete the work.

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