8 workers can build a house in 30 days. How many workers are needed if the house is to be built in 10 days?

The problem involves finding how many workers are needed to complete a job in fewer days, given that the number of workers and the time taken to complete the job are inversely proportional.

Here's the step-by-step solution:

1. Let the number of workers needed to build the house in 10 days be \( x \).
2. According to the problem, 8 workers can build the house in 30 days.
3. The relationship between the number of workers and the time to complete the job can be written as:
   \[
   \text{Workers} \times \text{Days} = \text{Constant Amount of Work}
   \]
   For the given dataThe problem involves finding how many workers are needed to complete a job in fewer days, given that the number of workers and the time taken to complete the job are inversely proportional.

Here's the step-by-step solution:

1. Let the number of workers needed to build the house in 10 days be \( x \).
2. According to the problem, 8 workers can build the house in 30 days.
3. The relationship between the number of workers and the time to complete the job can be written as:
   \[
   \text{Workers} \times \text{Days} = \text{Constant Amount of Work}
   \]
   For the given 
   \[
   8 \times 30 = x \times 10
   \]
4. Solving for \( x \):
   \[
   240 = 10x
   \]
   \[
   x = \frac{240}{10} = 24
   \]

So, 24 workers are needed to build the house in 10 days.

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

Here are 5 related questions to further explore the topic:
1. What if 16 workers were assigned the task? How many days would they take?
2. If the workers were reduced to 4, how long would it take to build the house?
3. How many houses could 24 workers build in 30 days?
4. What if the workers' efficiency dropped by 25%? How would that affect the time taken?
5. How many workers would be needed to build the house in 20 days?

**Tip:** When solving problems involving work, time, and workers, remember that these quantities are often inversely proportional. More workers typically means less time to complete the task.

Find out how many workers are needed to build a house in 10 days when 8 workers can do it in 30 days. This solution covers the inverse relationship between workers and time, using the formula Workers × Days = Constant Amount of Work. Perfect for students in Grades 6-8.

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