If "n" persons do a job in "d" days, in how many days do "n+m" persons do the same job?

Answer 1

jobs per man-days is
j/nd= j/(n+m)x where x is the pro-rated number of days given
n+m persons and based on the rate of 1job/nd man-days

x=nd/(n+m) days for n+m persons to do job

Answer 2

n people do 1 job in d days. So in 1 day, n people do 1/d jobs. That means in 1 day, one person does 1/dn jobs.

Now we know there are n+m people. Each day, the do (n+m)/dn jobs. Let a be the number of days it takes them to do a job. Then...

a(n+m)
- - - - - - - = 1
dn

a(n+m) = dn

dn
-------- = a
(n + m)

So it takes n+m men (dn)/(n+m) days to do the same job.

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Example:
Say 3 men can do a job in 4 days.
How many days can 5 men do the same job? (n=3,d=4,m=2)

3 men can do 1/4 of the job in a day.
1 man can do 1/12 of the job in a day.
5 men can do 5/12 of the job in a day.
Therefore, 5 men can do the job in 12/5 days, or 2.2 days.

Plugging in our formula (4*3)/(3+2) = 12/5, so the answer holds.

Answer 3

Use an inverse proportion:

Let the number of days sought be D. then

n * d = (n+m) * D

Solve for D.

Example:

If 1 person can do a job in 9 days, how long will it take 1+2 people to do the job?

1 * 9 = 3 * D
D = 3

Answer 4

if n people do it in d days and m do it in e days then n/d n+m/d-e
dn+dm=dn-en
dm=-en

so dm/n=-e
therefore d-dm/n days to do same job