8 workers together at the same rate finished a painting job in 5 hours. hour long would it take 12 such workers working at the same rate to finish the same job? each worker finished____(fraction) of the job in one hour. 12 workers finished_____(fraction) of the job in one hour, they finished the job in_____hours
Simple.
it takes 40 'workerhours' to do the job.
so if 12 'workers' do it, it would take 40/12 hours or 3 hours and 20 minutes.
To find the answer, we can use the concept of worker-hours. We know that 8 workers finished the painting job in 5 hours. This means they did a total of 8 workers x 5 hours = 40 worker-hours.
To determine how long it would take 12 workers to finish the same job at the same rate, we can divide the total worker-hours needed by the number of workers. In this case, we divide 40 worker-hours by 12 workers.
40 worker-hours ÷ 12 workers = 3.33 worker-hours
Therefore, it would take 12 workers approximately 3 hours and 20 minutes to finish the job.
Now let's calculate the fraction of the job done by each worker in one hour. Since there are 8 workers, and they finished the job in 5 hours, each worker contributed a fraction of 1/8 of the job in one hour.
For 12 workers, we can use the same logic. Since it takes them 3.33 worker-hours to finish the job, we divide this by the number of workers to find their individual contribution.
3.33 worker-hours ÷ 12 workers = 0.2775 worker-hours per worker
This means that each worker contributes approximately 0.2775 worker-hours towards the job in one hour.
To find the fraction of the job done by each worker in one hour, we can divide their contribution by the total worker-hours needed to finish the job:
0.2775 worker-hours ÷ 40 worker-hours = 0.0069375
So, each worker finishes approximately 0.0069375 or 0.69% of the job in one hour.
Finally, since we now know that each worker finishes 0.0069375 of the job in one hour, and there are 12 workers, we can multiply these values:
0.0069375 per worker x 12 workers = 0.08325
Therefore, 12 workers finish approximately 0.08325 or 8.32% of the job in one hour.
And since we already calculated that it takes 3.33 worker-hours for them to finish the job, we can say that 12 workers finish the job in approximately 3 hours and 20 minutes.