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Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job \$8\$ days earlier. If the job needs to completed \$28\$ days earlier, how many additional workers should be hired?

Dec 12, 2023

### 2+0 Answers

#1
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Let n be the number of additional workers needed. Let x be the original number of days needed to complete the job with 5 workers.

We can set up two equations based on the given information:

With 5 workers: 5x is the total amount of work done.

With 6 workers: They can finish the job in x−8 days. So, 6(x−8) is the total amount of work done.

Since the total amount of work required for the job is the same regardless of the number of workers, we can set the two expressions equal to each other:

5x=6(x−8)

Simplifying and solving for x:

5x=6x−48 x=48

This means that originally, the job would take 48 days to complete with 5 workers.

Now, we need to find the number of additional workers needed to complete the job 28 days earlier. We can set up another equation based on this information:

5x=6(x−28)

Substituting x=48:

5⋅48=6(48−28) 240=6⋅20

This means that the total amount of work required for the job is 240 work units.

We can set up one more equation to find the number of additional workers needed:

6(x−28)=n(x−28)

Substituting x=48 and 240 for the total work:

6(48−28)=n(48−28) 120=20n n=16​

Therefore, 16 additional workers should be hired to complete the job 28 days earlier.

Dec 12, 2023
#2
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so, basically, say x is the amount of days 1 person can do the task in. then x/5-x/6=8, meaning x=240, and 5 workers take 48 days, so if you want to take 20 days, you have to have 12 workers. 12-5 = 7, so you need 7 extra workers!

Dec 12, 2023