https://r2.erweima.ai/mathbot/image/1725922134853rx7aogc5.jpg

The problem presented involves a three-part proportional relationship (regra de três), which can be solved step by step.

### Given Data:

- **Original condition**:
  - 50 workers
  - 7 hours per day
  - 26 days
  - 400 meters of wall
  - Difficulty level: 3

- **New condition**:
  - Workers decreased by 20%: \(50 \times (1 - 0.2) = 40 \) workers
  - 8 hours per day
  - 30 days
  - Difficulty level reduced to 1

### Step-by-step solution:

1. **Calculate the original work rate** (productivity):
   The total work is 400 meters of wall with 50 workers, working 7 hours per day for 26 days, and at difficulty level 3. The relation can be expressed as:
   \[
   \text{Work done} = \frac{50 \times 7 \times 26}{3}
   \]

2. **New work rate**:
   In the new situation, the number of workers is reduced by 20% (so 40 workers), they work 8 hours per day for 30 days, and the difficulty level is reduced to 1. The relation becomes:
   \[
   \text{New work done} = 40 \times 8 \times 30
   \]

3. **Determine the proportional relationship**:
   The amount of work is directly proportional to the number of workers, the number of hours per day, and the number of days. It is inversely proportional to the difficulty level.

   So, the new wall length can be found by using:
   \[
   \text{New wall length} = \text{Old wall length} \times \frac{40 \times 8 \times 30 / 1}{50 \times 7 \times 26 / 3}
   \]

4. **Simplify the expression**:
   \[
   \text{New wall length} = 400 \times \frac{40 \times 8 \times 30}{50 \times 7 \times 26} \times \frac{3}{1}
   \]

Now, let me calculate the result.The approximate new wall length that can be built is 1266 meters. Therefore, the correct answer is option **c. ≈ 1266 metros**.

Would you like further details or explanations? Here are some related questions to consider:

1. How would the result change if the difficulty level remained the same?
2. What if the number of workers were further reduced by 10%?
3. How is the result affected by increasing the hours worked per day to 9 instead of 8?
4. How would the calculation change if the project duration was reduced to 20 days?
5. How does the inverse proportionality of difficulty influence the final result?

**Tip:** Always check for direct and inverse proportional relationships in similar problems to set up the equation correctly.

Resolva a regra de três a seguir: 50 operários trabalhando 7 horas por dia, durante 26 dias, fazem 400 metros de parede com grau de dificuldade 3. Se diminuirmos o número de operários em 20%, trabalhando 8 horas por dia durante 30 dias, quantos metros aproximados de parede serão feitos se o grau de dificuldade cair para 1?

Solve a proportionality problem involving 50 workers building a wall under different conditions. Learn how changes in the number of workers, hours, days, and difficulty level affect the total work done. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation