Six people working 8 hours a day take ten days to finish a certain job. How long will it take for two people working 12 hours per day to finish the same job?
Understand the Problem
The question is a word problem asking us to calculate the time taken to complete a job given the number of people working, the number of hours worked per day, and the number of days. The task is to compute the time it takes for a different number of people working a different number of hours per day to complete the same job. The key concept here is to understand the inverse relationship between the number of people, the hours worked per day, and the number of days to complete the work.
Answer
20 days
Answer for screen readers
20 days
Steps to Solve
- Calculate the total work done by the first group
To find the total work done, multiply the number of people, the hours per day, and the number of days:
$TotalWork = NumberOfPeople \times HoursPerDay \times NumberOfDays$ $TotalWork = 6 \times 8 \times 10 = 480$
- Calculate the number of days for the second group
Let $x$ be the number of days it takes for the second group to complete the same job. We can set up the equation:
$2 \times 12 \times x = 480$
- Solve for x
Simplify and solve for $x$:
$24x = 480$ $x = \frac{480}{24} = 20$
Therefore, it will take 20 days for two people working 12 hours per day to finish the same job.
20 days
More Information
The total amount of work remains constant even when the number of people and hours worked per day change.
Tips
A common mistake is to assume a direct relationship instead of an inverse relationship. For example, some might assume that if the number of people decreases, the number of days also decreases. This is incorrect because with fewer people, it will naturally take more days to complete the same amount of work, assuming the same work rate.
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