A house is built by 20 workers in 30 days. How many workers will be needed to complete the work in 15 days?

20

40

45

52

This problem involves the concept of inverse proportionality. If the number of workers increases, the number of days required to complete the work decreases, assuming the work done per day remains constant.

We can solve this using the formula for inverse proportion:

\[
\text{Workers}_1 \times \text{Days}_1 = \text{Workers}_2 \times \text{Days}_2
\]

Given:
- Workers₁ = 20 workers
- Days₁ = 30 days
- Days₂ = 15 days

We need to find Workers₂ (the number of workers required to complete the house in 15 days).

\[
20 \times 30 = \text{Workers}_2 \times 15
\]

Solving for Workers₂:

\[
\text{Workers}_2 = \frac{20 \times 30}{15} = \frac{600}{15} = 40
\]

Thus, **40 workers** will be needed to complete the work in 15 days.

### Answer: 40

Would you like more details on this, or do you have any other questions?

Here are 5 related questions to expand on this topic:
1. If 40 workers can finish the job in 15 days, how many days would 10 workers take?
2. What if 25 workers were available? How long would it take them to finish the job?
3. If the workers increase their efficiency by 20%, how would that affect the number of workers needed for 15 days?
4. How many workers would be required to complete the house in 10 days?
5. If 30 workers were available, how many days would it take to finish the house?

**Tip:** Always remember that in inverse proportionality, as one variable increases, the other decreases accordingly.

A house is built by 20 workers in 30 days. How many workers will be needed to complete the work in 15 days?

Learn how to calculate the number of workers needed to complete a house-building job in 15 days instead of 30. This problem involves inverse proportionality, using the formula Workers₁ × Days₁ = Workers₂ × Days₂. A step-by-step solution is provided for students in Grades 6-8.

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