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

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In summary: If the job needs M man-days of work to be completed, thenn*t=MCan you use the information given to write down two more equations that involve n, t, and M?Yes.n*t=MAlso (n+3)(t-2)=M and (n+12)(t-5)=m
  • #1
agoogler
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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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  • #2
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
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
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!
 
  • #5
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.
 

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

1. How do you solve a work word problem?

To solve a work word problem, you need to first identify the known and unknown variables. Then, use the formula "work = rate x time" to set up an equation and solve for the unknown variable.

2. What is the formula for solving a work word problem?

The formula for solving a work word problem is "work = rate x time". This formula represents the relationship between the amount of work done, the rate at which the work is done, and the time it takes to complete the work.

3. How do you determine the number of men deployed by a contractor in a work word problem?

In a work word problem, the number of men deployed by a contractor can be determined by dividing the total amount of work by the rate at which the work is done. This will give the number of men needed to complete the work in the given time frame.

4. What are the key steps to solving a work word problem?

The key steps to solving a work word problem are: 1. Identify the known and unknown variables.2. Set up an equation using the formula "work = rate x time".3. Solve for the unknown variable.4. Check your answer to ensure it makes sense in the context of the problem.

5. Can you provide an example of solving a work word problem to find the number of men deployed by a contractor?

Yes, for example, if a contractor needs to complete a construction project that requires 360 hours of work and the rate of work for each man is 6 hours per day, then the number of men deployed by the contractor would be 360 / 6 = 60 men.

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