Four workers can build a house in 9 days. How many days would it takes 3 workers to build the same house?

Answer

To solve the problem of how many days it would take for 3 workers to build the same house, we can follow these steps:

### Step 1: Determine the total work done by the workers
We know that 4 workers can complete the house in 9 days. Therefore, we can calculate the total amount of work in terms of "worker-days".

\[ \text{Total work} = \text{Number of workers} \times \text{Number of days} = 4 \text{ workers} \times 9 \text{ days} = 36 \text{ worker-days} \]

### Step 2: Calculate the work done by one worker in one day
Since the total work is 36 worker-days, we can find out how much work one worker does in one day.

\[ \text{Work done by one worker in one day} = \frac{1 \text{ house}}{36 \text{ worker-days}} = \frac{1}{36} \text{ of the house} \]

### Step 3: Set up the equation for 3 workers
Now, we need to find out how many days (let's call this \(D\)) it would take for 3 workers to complete the same house. The total work done by 3 workers in \(D\) days can be expressed as:

\[ \text{Work done by 3 workers in } D \text{ days} = 3 \text{ workers} \times D \text{ days} = 3D \text{ worker-days} \]

### Step 4: Equate the work done to the total work
Since the total work required to build the house is 36 worker-days, we can set up the equation:

\[ 3D = 36 \]

### Step 5: Solve for \(D\)
Now, we can solve for \(D\):

\[ D = \frac{36}{3} = 12 \]

### Conclusion
Thus, it would take 3 workers a total of **12 days** to build the house.

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