10 workers can complete a job in 24 days, how many workers are required to complete the same job in 18 days?

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To determine the number of workers required to complete the same job in a different number of days, we can use the concept of work done (measured in worker-days).

1. **Calculate the total amount of work needed:**
   - If 10 workers can complete the job in 24 days, the total work required is:
     \[
     \text{Total Work} = \text{Number of Workers} \times \text{Number of Days} = 10 \times 24 = 240 \text{ worker-days}
     \]

2. **Determine the number of workers required to complete the job in 18 days:**
   - Let \(W\) be the number of workers required to complete the job in 18 days.
   - Since the total work required is still 240 worker-days, we can set up the equation:
     \[
     W \times 18 = 240
     \]
   - Solve for \(W\):
     \[
     W = \frac{240}{18} = \frac{240}{18} = 13.\overline{3}
     \]
   - Since the number of workers must be a whole number, we round up to the next whole number, which means 14 workers are required.

Therefore, 14 workers are required to complete the job in 18 days.

Would you like further details or have any questions?

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Here are some related questions that might interest you:

1. What is the formula for calculating the total amount of work needed for a job?
2. How does changing the number of workers affect the completion time of a job?
3. What is the concept of worker-days and how is it used in project management?
4. Can you explain the relationship between work, time, and number of workers?
5. How do you solve for a variable in an equation involving fractions?
6. What are some real-life applications of the worker-days concept?
7. How do you handle rounding in practical mathematical problems?
8. What strategies can be used to optimize workforce allocation for a project?

**Tip:** Always consider rounding up to the next whole number when dealing with quantities that cannot be fractional, such as the number of workers.

Explore how to calculate the number of workers required to complete a job in different time frames using worker-days concept. Understand the relationship between work, time, and workforce allocation. Suitable for high school students and project managers.

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