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The problem presents a sequence of workers increasing daily, and asks how long the same task would take if completed by 40 workers who are 50% less efficient.

### Step-by-step breakdown:

#### 1. The Sequence of Workers:
- Day 1: 2 workers
- Day 2: 6 workers
- Day 3: 12 workers
- Day 4: 20 workers
- Final day: 72 workers

This follows a pattern where the number of workers each day increases. The challenge is to find out how many days the work would take if done with 40 workers, who are 50% less efficient.

#### 2. Analyzing the original case:
- The number of workers each day increases by a certain amount.
- To find the total amount of work done in terms of "worker-days" (the total contribution of workers each day), we can sum the number of workers over the entire period.
  
Let’s calculate the sum of workers from Day 1 to the final day where 72 workers are involved. After this, we’ll compare it with the scenario involving 40 workers working at 50% efficiency.

I will now calculate these values and present the results.The total amount of work done in the original scenario, in terms of "worker-days," is 300 worker-days.

If 40 workers, who are 50% less efficient (equivalent to 20 effective workers), were to perform the same task, the work would be completed in approximately 15 days.

### Do you have any questions or need more details?

Here are 5 related questions you might consider:
1. How does the arithmetic progression in the workers' count impact the total work done?
2. What are "worker-days," and why are they important in calculating labor efficiency?
3. How would the completion time change if the efficiency drop were different, e.g., 25% less efficient?
4. Can you calculate how long it would take if the original group worked with a consistent number of workers each day?
5. How would changing the initial and final number of workers affect the overall completion time?

#### Tip: 
When dealing with efficiency problems, converting everything to "work-units" or "worker-days" can help simplify comparisons between different scenarios.

Una obra es efectuada de la manera siguiente: el 1er día laboran 2 obreros, el 2do día laboran 6 obreros, el 3er día laboran 12 obreros, el 4to día laboran 20 obreros y así sucesivamente hasta que el último día laboran 72 obreros. Si toda la obra hubiera sido efectuada solo por 40 obreros 50% menos eficientes que los anteriores, ¿en cuántos días más o menos se hubiera culminado?

Explore how to calculate the time required to complete a task with changing numbers of workers in an arithmetic progression. Learn the step-by-step process to determine the total work done and how efficiency affects completion time. Suitable for high school students.

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