We can solve this problem using the concept of work rates. The key idea is that the amount of work done is constant, and it can be expressed in terms of worker-days (i.e., the number of workers multiplied by the number of days they work).

Step 1: Calculate the total amount of work.

The entire crew of 18 workers was originally scheduled to complete the job in 10 days. Therefore, the total work required to finish the project is:

$\text{Total work} = 18 \, \text{workers} \times 10 \, \text{days} = 180 \, \text{worker-days}.$

Step 2: Calculate the work done in the first 4 days.

In the first 4 days, all 18 workers were working. The amount of work they completed during this time is:

$\text{Work done in 4 days} = 18 \, \text{workers} \times 4 \, \text{days} = 72 \, \text{worker-days}.$

Step 3: Calculate the remaining work after 4 days.

The remaining work after the first 4 days is:

$\text{Remaining work} = 180 \, \text{worker-days} - 72 \, \text{worker-days} = 108 \, \text{worker-days}.$

Step 4: Determine the work rate of the reduced crew.

Let $x$ represent the number of workers who were moved to another project. The remaining number of workers is $18 - x$. The rest of the crew needed 12 more days to finish the job, meaning they completed the remaining 108 worker-days of work in 12 days. Thus, we can set up the following equation:

$(18 - x) \times 12 = 108.$

Step 5: Solve for $x$.

Simplify the equation:

$18 - x = \frac{108}{12} = 9.$

$x = 18 - 9 = 9.$

Final Answer:

9 workers were removed from the crew.

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Would you like more details or have any questions?

Here are 5 questions that extend this concept:

1. What if the initial crew had 20 workers instead of 18, how many workers would have been removed?
2. If the rest of the crew finished the remaining work in 8 days instead of 12, how many workers were removed?
3. How would the solution change if the total amount of work was 200 worker-days instead of 180?
4. What if the crew was reduced to 10 workers, how many additional days would be needed to complete the work?
5. Can you express the total work required as a function of the initial number of workers and the number of days?

Tip: When dealing with work rate problems, always think in terms of total worker-days. This helps to balance the amount of work with the changing number of workers or time.