# Work word probem

1. Jun 24, 2013

1. The problem statement, all variables and given/known data

A contractor employed a certain number of men to complete a work in a certain number of days. If 3 more men were deployed the work would be ﬁnished 2 days earlier while
if 12 more men were deployed it would be ﬁnished 5 days earlier. Find number of men
deployed by the contractor.

2. Relevant equations

3. The attempt at a solution
Let the number of men be n. Let the number of days be t.

2. Jun 24, 2013

### Office_Shredder

Staff Emeritus
If the job needs M man-days of work to be completed, then
n*t = M

Can you use the information given to write down two more equations that involve n, t, and M?

3. Jun 24, 2013

### verty

These problems are nasty, the type that I hate the most, needing one to use variables and needing simultaneous equations to solve.

Think of units of work: 1 worker working for 1 day does 1 unit of work. Units of work per day is how we measure how productive a team is. Now let M be the number of units of work required to complete the project. This is exactly in line with what Office_Shredder said.

4. Jun 25, 2013

Yes.
n*t=M
Also (n+3)(t-2)=M and (n+12)(t-5)=m
And ... I just solved this simultaneous equations to get n=12 and t=10 which is the correct answer.
Thanks a lot for help!

5. Jun 25, 2013

### HallsofIvy

Staff Emeritus
In other words, all of algebra?