If 30 men working 9 hours per day can reap a field in 16 days, how many men will be required to reap the field in 15 days, working 8 hours per day?

To solve this problem, we'll use the concept of work, which can be expressed in terms of the number of men, the number of days, and the number of hours per day they work.

### Step-by-Step Solution

#### Given:
- 30 men can reap the field in 16 days working 9 hours per day.
- We need to find out how many men (\(x\)) are required to reap the field in 15 days, working 8 hours per day.

#### Step 1: Calculate the total amount of work
- The total work done (in terms of "man-hours") can be calculated by multiplying the number of men, the number of days, and the number of hours per day.

  \[
  \text{Total Work} = 30 \times 16 \times 9 = 4320 \text{ man-hours}
  \]

#### Step 2: Set up the equation for the new scenario
- In the new scenario, the number of men is \(x\), the number of days is 15, and the number of hours per day is 8.
- The total work remains the same, so we set up the equation:

  \[
  x \times 15 \times 8 = 4320 \text{ man-hours}
  \]

#### Step 3: Solve for \(x\)
- Simplify the equation to find \(x\):

  \[
  120x = 4320
  \]

  \[
  x = \frac{4320}{120} = 36
  \]

### Answer:
36 men will be required to reap the field in 15 days, working 8 hours per day.

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**Related Questions**:
1. How many days will it take 25 men to reap the field working 10 hours per day?
2. If the number of men is doubled, how many days would it take them to reap the field, working the same number of hours?
3. What would happen if the men worked only 6 hours per day? How many men would be required to complete the work in 15 days?
4. How many hours per day should 30 men work to finish reaping the field in 12 days?
5. If 40 men work 7 hours per day, how many days will it take to complete the work?

**Tip**: Always keep in mind that work is proportional to the number of workers, the number of hours worked per day, and the number of days worked. Adjust any of these factors, and the other factors must adjust accordingly to complete the same amount of work.

Learn how to calculate the number of men required to reap a field in 15 days, working 8 hours per day. This problem involves understanding proportional relationships and work-time calculations. Suitable for students in Grades 9-12.

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