MHB How many people need to be added to complete the project in 5 days?

[Monoxdifly]

A project can be done in 35 days by 12 people. However, after 25 days the project paused for 5 days. How many people need to be added?

I guess it's 12. Am I right?

 

[MarkFL]

After 25 days, 2/7 of the job is left to be done. 1 person can do 2/7 of the job in 120 days, so it would take 120/5 = 24 people to do 2/7 of the job in 5 days, so yes, 12 people need to be added. :D

 

[Monoxdifly]

How did you get that 120 days?

 

[MarkFL]

How did you get that 120 days?

1 person can do the entire job in 12*35 = 420 days, so it would take 1 person (2/7)(420) = 120 days to do 2/7 of the job.

 

[Monoxdifly]

Sorry, I did a typo in the first post. It should be like this:

A project can be done in 35 days by 12 people. However, after 24 days the project paused for 5 days. How many people need to be added?

I guess it's 12. Am I right?

Being said, guess 12 isn't correct.

 

[HallsofIvy]

So "after 24 days" rather than "after 25 days"? That's odd- it just makes the numbers messier. Do the same thing MarkFl did. 24/35 of the job has already been done. In order that the job still be completed in the full 35 days, we must complete the 1- 24/35= 11/35 of the job in the remaining 6 days. That means we must complete (11/35)/6= 11/210 job per day. Since the original 12 people could do the job in 35 days, each person works at 1/(35*12)= 1/420 "job per day". To do 11/210 job at a rate of 1/420 job per person, we must have (11/210)/(1/420)= (11/210)(420/1)= 22 people. We must add 22- 12= 10 new people.

 

[Monoxdifly]

So, basically the calculation is $$\frac{12\times(35-(24+5)+5)}{6}$$?

 

[physiclawsrule]

25/35 of the project is completed
12 people can do 1/35 a day
you need to do 10/35 in 5 days
12 people can do 5/35 in 5 days
so you need twice as more people