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This problem involves calculating the number of days 10 workers, working 8 hours per day, will take to build the remaining 50 meters of a wall, given that 8 workers built 30 meters of the wall in 9 days, working 6 hours per day.

### Step-by-Step Solution:

1. **Determine the rate of work for the first group:**
   - 8 workers complete 30 meters in 9 days, working 6 hours per day.
   - Total hours worked = \( 8 \text{ workers} \times 9 \text{ days} \times 6 \text{ hours/day} = 432 \text{ total work hours} \).
   - The rate of work for 8 workers is \( \frac{30 \text{ meters}}{432 \text{ hours}} = \frac{30}{432} \text{ meters/hour} \), or simplified, \( \frac{5}{72} \text{ meters/hour} \).

2. **Determine the rate of work for 1 worker:**
   - The rate for 1 worker is \( \frac{5}{72 \times 8} = \frac{5}{576} \text{ meters/hour} \).

3. **Determine the rate of work for the second group of workers:**
   - 10 workers work 8 hours per day.
   - The rate for 10 workers is \( 10 \times \frac{5}{576} = \frac{50}{576} = \frac{25}{288} \text{ meters/hour} \).

4. **Calculate the total hours needed to complete the 50 meters:**
   - Total hours needed = \( \frac{50 \text{ meters}}{\frac{25}{288} \text{ meters/hour}} = 50 \times \frac{288}{25} = 576 \text{ hours} \).

5. **Determine the number of days required:**
   - The workers are working 8 hours per day, so the total days required = \( \frac{576 \text{ hours}}{10 \times 8 \text{ hours/day}} = \frac{576}{80} = 7.2 \) days.

### Answer:
The 10 workers will need **7.2 days** (or approximately 7 days and 2 hours) to complete the remaining 50 meters of the wall.

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Would you like further details or have any questions?  
Here are some related questions to expand on this concept:

1. What would happen if the number of workers doubled to 20 for the remaining wall?
2. How would the time change if the workers only worked 5 hours per day?
3. What is the total amount of work done by all workers in hours for the entire wall (30m + 50m)?
4. How would the calculation differ if the number of workers varied each day?
5. Can you model the total work as a function of worker efficiency, hours, and meters?

**Tip:** Always break complex problems into smaller, manageable steps, especially when dealing with multiple variables like workers, hours, and units of work.

Si 8 obreros realizan en 9 días trabajando a razón de 6 horas por día un muro de 30 m. ¿Cuántos días necesitarán 10 obreros trabajando 8 horas diarias para realizar los 50 m de muro que faltan?

Learn how to calculate the time required for 10 workers, working 8 hours a day, to build a 50m wall, given that 8 workers built 30m in 9 days, working 6 hours per day. This problem involves key mathematical concepts such as work rate and proportions, ideal for students in Grades 9-12.

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