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

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Homework Help Overview

The problem involves a contractor employing a certain number of men to complete a project within a specified number of days. The scenario presents two conditions where additional men can reduce the completion time, leading to a need for formulating equations based on these conditions.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to establish variables for the number of men and days, seeking guidance on translating the problem into equations. Some participants suggest using the concept of man-days to formulate additional equations based on the conditions provided.

Discussion Status

Participants are actively discussing how to set up the equations needed to solve the problem. There is recognition of the complexity involved in using variables and simultaneous equations. Some have proposed specific equations based on the problem's conditions, while others express frustration with the problem type.

Contextual Notes

There is a mention of the need for simultaneous equations and the challenge of translating the problem into a solvable format. The discussion reflects a shared sentiment regarding the difficulty of the problem type.

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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!
 
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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?
 
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.
 
Office_Shredder said:
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!
 
verty said:
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.
 

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