Thirty workers working eight hours a day take six days to complete a certain job. How many days would fifty such workers working for six hours a day take to complete the same job?
Answer (2)
It would take approximately 5 days for fifty workers working six hours each day to complete the same job. This is calculated based on the total work done in worker-hours from the initial scenario. The total work required is 1440 worker-hours, and with 50 workers working 6 hours a day, they can complete the job in 5 days.
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To solve this problem, we'll use the concept of total 'worker-hours' required to complete the job.
Step-by-Step Solution:
Calculate the total work in worker-hours :
Initially, 30 workers working 8 hours a day for 6 days complete the job.
Calculate the total worker-hours: Total worker-hours = 30 workers × 8 hours/day × 6 days = 1440 worker-hours
Determine how long it would take 50 workers working 6 hours a day to complete the same job :
Let the number of days required be x .
The number of worker-hours they can provide per day is: 50 workers × 6 hours/day = 300 worker-hours/day
Set up the equation for total work: 300 worker-hours/day × x days = 1440 worker-hours
Solve for x : x = 300 1440 = 4.8 days
Conclusion:
It would take 50 workers working 6 hours a day approximately 4.8 days to complete the same job. Depending on how you round, you might interpret this as needing either 5 full days or 4 full days plus part of a day.
