SOLUTION: Hi 5 workers complete a job in 6 days. After 2 days, 3 workers left. how many more days will the job take the remaining workers. Thanks

Question 1052648: Hi
5 workers complete a job in 6 days. After 2 days, 3 workers left.
how many more days will the job take the remaining workers.
Thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
5 workers complete the job in 6 days.

after 2 days, 3 workers leave.

how many more days for the remaining workers to complete the job?

the assumption here is that all the workers work at the same rate.

the basic formula is:

n * r * t = q

n = numbr of workers
r = rate of each worker
t = time
q = quantity

you are given that n = 5 and t = 6 and q = 1

q = 1 means 1 job is to be completed.

the formula becomes:

5 * r * 6 = 1

solve for r to get r = 1/30

4 = 1/30 means when all 5 men work for 6 days, each worker completes 1/30 of the job per day.

when r = 1/30, 5 * r * 6 = 1 becomes 5 * 1/30 * 6 = 1 which becomes 1 = 1 which confirms the value for r is correct.

problem states you have 5 people working for 2 days and then 2 people working for the rest of the time.

you want to know how long is the rest of the time.

the formula becomes:

(5 * 1/30 * 2) + (2 * 1/30 * t) = 1

the formula says that 5 people working at the rate of 1/30 of the job per person per day for 2 days and then 2 people working at the rate of 1/30 of the job per person per day for t days will complete the job in t + 2 days.

you need to solve for t.

simplify the equation to get 10/30 + 2/30 * t = 1

subtract 10/30 from both sides of the equation to get 2/30 * t = 20/30

multiply both sides of the eqution by 30/2 to get t = 20/30 * 30/2

simplify to get t = 10.

the 2 people remaining will need to work an additional 10 days to complete the job.

the final equation becomes:

5 * 1/30 * 2 + 2 * 1/30 * 10 = 1

simplify to get 10/30 + 30/30 = 1 which becomes 1 = 1, confirming the solution is correct.

the total time it takes is 2 days when 5 people were working plus an additional 10 days when only 2 people were working for a total of 12 days to complete the job.,

you were asked how many more days to complete the job.

that would be 10 more days,

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