Thirty men take 20 days to complete a job working 9 hours a day. How many hours a day should 40 men work to complete the job?

To determine how many hours a day 40 men should work to complete the job, we can use the concept of man-hours.

First, calculate the total number of man-hours required to complete the job with the initial group of men:

\[ \text{Total man-hours} = \text{Number of men} \times \text{Number of days} \times \text{Number of hours per day} \]

Given:
- 30 men
- 20 days
- 9 hours per day

\[ \text{Total man-hours} = 30 \times 20 \times 9 = 5400 \text{ man-hours} \]

Now, we need to determine how many hours a day 40 men should work to complete the same amount of work. Let \( h \) be the number of hours per day the 40 men need to work. 

Since the total man-hours required remains the same, we set up the equation:

\[ 40 \times d \times h = 5400 \]

To find the number of hours per day (\( h \)), we need to know the number of days (\( d \)). Assuming the 40 men are to complete the job in the same 20 days, we get:

\[ 40 \times 20 \times h = 5400 \]

Solving for \( h \):

\[ 800h = 5400 \]

\[ h = \frac{5400}{800} \]

\[ h = 6.75 \]

Thus, 40 men should work 6.75 hours a day to complete the job in 20 days.

Would you like more details or have any other questions? Here are some other problems you might consider:

1. If 50 men were to complete the job, how many hours a day should they work?
2. If the 40 men work 8 hours a day, how many days will it take to complete the job?
3. How many men are needed to complete the job in 10 days working 9 hours a day?
4. If the job was completed in 18 days by 35 men, how many hours a day did they work?
5. If the number of men increased by 10 each day, how long would it take to complete the job working 9 hours each day?

**Tip:** When solving problems involving work and time, always check the total work in terms of man-hours to maintain consistency across different scenarios.

Learn how to calculate the number of hours per day 40 men should work to complete a job based on proportional reasoning and man-hours. This problem involves 30 men completing a job in 20 days working 9 hours a day.

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