Final answer:
If 12 assemblers can complete a job in 6 hours, it would take 9 assemblers 8 hours to complete the same job, having calculated the rate of work and then determined the time taken for the reduced number of assemblers to complete that work.
Step-by-step explanation:
If 12 assemblers can complete a certain job in 6 hours, and you want to know how long the same job will take if the number of assemblers is reduced to 9, you need to calculate the total work done and then determine the time taken by the 9 assemblers to complete the same amount of work.
First, we find the amount of work done by one assembler in one hour, which we can call the rate of work. Since 12 assemblers take 6 hours to complete the job, one assembler would take 12 times longer. So, one assembler would take 12 * 6 = 72 hours to complete the job alone. Therefore, the rate of work for one assembler is 1/72 of the job per hour.
Now, if you have 9 assemblers working together at the rate of 1/72 of the job per hour, you can multiply the individual rate by the number of assemblers to find the new rate of work: 9/72 of the job per hour, which simplifies to 1/8 of the job per hour.
To find how many hours it will take these 9 assemblers to complete the entire job, you can divide the job (1) by the rate (1/8): 1 รท (1/8) = 8 hours. Hence, 9 assemblers will complete the job in 8 hours.