If 18 assemblers can complete a certain job in 6 ​hours, how long will the same job take if the number of assemblers is cut back to 12​? answer in decimal

This problem involves an inverse proportionality because the number of assemblers and the time taken to complete the job are inversely related. As the number of assemblers decreases, the time taken to complete the job increases.

Let's solve this step-by-step:

### Step 1: Set up the relationship
Let:
- \( T_1 = 6 \) hours (time taken by 18 assemblers),
- \( N_1 = 18 \) assemblers,
- \( N_2 = 12 \) assemblers,
- \( T_2 \) be the time it takes for 12 assemblers to complete the job.

The relationship between the number of assemblers and the time is given by:
\[
N_1 \times T_1 = N_2 \times T_2
\]

### Step 2: Solve for \( T_2 \)
Substitute the known values into the equation:
\[
18 \times 6 = 12 \times T_2
\]

Simplify:
\[
108 = 12 \times T_2
\]

Now solve for \( T_2 \):
\[
T_2 = \frac{108}{12} = 9
\]

So, the job will take **9 hours** if the number of assemblers is reduced to 12.

Would you like more details or have any questions? 

Here are 5 related questions for deeper understanding:
1. What if the number of assemblers increased to 24? How long would the job take?
2. If it took 9 hours for 12 assemblers, how many assemblers would be needed to finish the job in 4 hours?
3. How does the relationship between time and the number of workers affect project planning?
4. Can we use this method if the number of workers is not constant throughout the job?
5. How would overtime (extra hours worked by the same assemblers) affect job completion time?

**Tip:** In problems involving workers or machines completing tasks, time and the number of workers are often inversely proportional.

Find out how long it takes for 12 assemblers to complete a job if 18 assemblers can do it in 6 hours. This problem demonstrates the inverse proportionality relationship between the number of workers and the time taken to complete a task. Suitable for Grades 6-8 students, with a step-by-step solution provided.

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