Solve Work Word Problem: Find Number of Men Deployed by Contractor

[agoogler]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

Let the number of men be n. Let the number of days be t.
Now how should I translate this problem into equation ? Please help!

 

[Office_Shredder]

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?

 

[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.

 

[agoogler]

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?

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!

 

[HallsofIvy]

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

In other words, all of algebra?

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.