2 men or 3 women can complete a job in 96 days. How many days would 6 men AND 7 women take to finish the job

We are given that:

- 2 men can complete the job in 96 days.
- 3 women can complete the job in 96 days.

Let’s first calculate the work rates of a man and a woman.

### Step 1: Calculate the work rate of 1 man and 1 woman.

1. **Work rate of 2 men**:
   Since 2 men take 96 days to complete the job, the rate of work for 2 men combined is:
   \[
   \frac{1}{96} \text{ jobs per day.}
   \]
   Therefore, the work rate of 1 man is:
   \[
   \text{Rate of 1 man} = \frac{1}{96} \div 2 = \frac{1}{192} \text{ jobs per day.}
   \]

2. **Work rate of 3 women**:
   Similarly, 3 women take 96 days to complete the job, so the combined work rate of 3 women is:
   \[
   \frac{1}{96} \text{ jobs per day.}
   \]
   Therefore, the work rate of 1 woman is:
   \[
   \text{Rate of 1 woman} = \frac{1}{96} \div 3 = \frac{1}{288} \text{ jobs per day.}
   \]

### Step 2: Calculate the total work rate of 6 men and 7 women.

- The combined work rate of 6 men is:
  \[
  \text{Rate of 6 men} = 6 \times \frac{1}{192} = \frac{6}{192} = \frac{1}{32} \text{ jobs per day.}
  \]

- The combined work rate of 7 women is:
  \[
  \text{Rate of 7 women} = 7 \times \frac{1}{288} = \frac{7}{288} = \frac{1}{41.14} \text{ jobs per day (approximately).}
  \]

### Step 3: Combine the work rates.

The total combined work rate of 6 men and 7 women is:
\[
\text{Total work rate} = \frac{1}{32} + \frac{1}{41.14} \approx 0.03125 + 0.0243 = 0.05555 \text{ jobs per day.}
\]

### Step 4: Calculate the time taken to finish the job.

The time taken to finish the job is the reciprocal of the total work rate:
\[
\text{Time taken} = \frac{1}{0.05555} \approx 18 \text{ days.}
\]

Thus, 6 men and 7 women together would take approximately **18 days** to finish the job.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What if only 3 men and 4 women worked together? How many days would it take?
2. How long would it take if 10 women were working alone?
3. Can you calculate the work rate of 4 men working with 5 women?
4. How would the time change if 2 additional men were added to the team?
5. How does the total work time change if each person works faster by 10%?

**Tip:** When combining rates, always make sure to add the individual rates before finding the total work time.

2 men or 3 women can complete a job in 96 days. How many days would 6 men AND 7 women take to finish the job?

Learn how to calculate the time it takes for 6 men and 7 women to finish a job when 2 men or 3 women can complete it in 96 days. This solution involves work rates and proportionality, with step-by-step calculations. Ideal for students in Grades 8-10.

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