How Many Workers and Days to Make 30 Units in 2 Days?

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Homework Help Overview

The problem involves determining the number of workers required to produce 30 units in 2 days, given that 2 workers can produce 10 units in 3 days. The subject area relates to work rate and productivity calculations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss setting up equations to relate workers, days, and units produced. Some express uncertainty about the correct approach and seek clarification on the equations to use. Others explore the concept of direct variation in relation to the problem.

Discussion Status

Some participants have proposed potential solutions and reasoning, while others have expressed doubts about their methods. There is an indication of productive discussion, with at least one participant affirming the reasoning of another regarding the calculation of workers needed.

Contextual Notes

Participants mention the need for clarity on the equations and methods suitable for this type of problem, indicating a focus on understanding rather than simply arriving at an answer.

Megasundato
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Homework Statement



It takes 2 workers 3 days to make 10 units. How many workers would it take to make 30 units in 2 days?

Homework Equations



I'm not sure of what equations to use.

The Attempt at a Solution



I've tried techniques such as laying out the equations and using substitution, but I'm really not sure how to work this particular problem.

I don't know if this is posted on another thread, if so, I would appreciate a link very much.
 
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Megasundato said:

Homework Statement



It takes 2 workers 3 days to make 10 units. How many workers would it take to make 30 units in 2 days?

Homework Equations



I'm not sure of what equations to use.

The Attempt at a Solution



I've tried techniques such as laying out the equations and using substitution, but I'm really not sure how to work this particular problem.

I don't know if this is posted on another thread, if so, I would appreciate a link very much.

Show us what you've tried, even if it's wrong.

Look at this in terms of what a single worker can do in one day.
 
ok. well pretty much I just set some equations up such as,

d*w=p
2w*3d=10p

But I realized this is not the right approach.

Just now in the writing of this post, I think I may have figured out how to do it. I made into a constant(k) type problem.

pretty much I put that the product varies directly with the amount of workers multiplied by the time in days.

p=kwd

I then just solved for constant, k, using the equation which gives me all the values of the variables. I got k = 5/3 and my answer for the problem was 9, which was a choice among 5, 6, 9, 18.

I do believe this the the correct method for this type of problem, but of course, please tell me if it is not. thanks.
 
I agree with your answer. Here is my reasoning.

One worker can make 5 units in 3 days, so each worker can make 5/3 unit per day.

So in 2 days, one worker can make 2*5/3 = 10/3 units. To make 30 units, you need 30/(10/3) = 30 * 3/10 = 9 workers.
 
that makes sense, thanks.
 

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