Solving a Group Job Efficiency Problem

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Discussion Overview

The discussion revolves around a group job efficiency problem involving the work rates of men and women. Participants are trying to determine how long it will take for a group of men and women to complete a job after a partial contribution from the men before the women join. The scope includes mathematical reasoning and problem-solving related to rates of work.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant calculates the work rates of women and men, stating that 48 women can complete the job in 16 days, resulting in a rate of 3 women/day, while 16 men can complete it in 24 days, leading to a rate of 2/3 men/day.
  • Another participant questions the interpretation of the work rate calculation, suggesting that it should be framed as the amount of work done per day rather than a direct rate.
  • A participant expresses confusion about how to incorporate the initial work done by the 10 men before the women join, seeking further advice on the problem.
  • One participant clarifies that if 48 women can do 1/16 of the job in one day, then one woman would take 1/(16*48) of the job in one day, and similarly for men, indicating that men do twice as much work as women.

Areas of Agreement / Disagreement

Participants are discussing different interpretations of work rates and how to approach the problem. There is no consensus on the best method to solve the problem, and confusion remains regarding the initial conditions and calculations.

Contextual Notes

Participants have not resolved how to effectively combine the work done by the men before the women joined, and there are differing views on how to express work rates and contributions over time.

blumfeld0
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Suppose it takes 48 women 16 days to do the same job that it takes 16 men to do in 24 days. If 10 men started working on the job and worked for 5 hours, then all 48 women joined them. how long would it take them working together to finish the job? i know i have to find the rates so i have

48/16= 3 women/day

16/24= 2/3 men/day

i am just having trouble knowing what to do with the fact that 10 men started working BEFORE the women joined. i could this problem easily if they both started working at the same time. thanks
 
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blumfeld0 said:
Suppose it takes 48 women 16 days to do the same job that it takes 16 men to do in 24 days. If 10 men started working on the job and worked for 5 hours, then all 48 women joined them. how long would it take them working together to finish the job?


i know i have to find the rates so i have

48/16= 3 women/day

16/24= 2/3 men/day

What do you mean by '48/16= 3 women/day'? It takes 48 women one day to do 1/16 of the job, right? Further on, it takes 16 men one day to do 1/24 of the job. See what you can do with that.
 
im still confused. i understand what you said.
i know 1/t1 + 1/t2 = 1/t total
any other advice


thanks
 
Well, If it takes 48 women 1 day to do 1/16 of the job, a one women, in one day, would take 1/(16*48). For 1 man in 1 day they could do 1/(16*24). From that you can see men do twice as much as women. The values i stated just before are for days, divide by 24 to get hours.
 

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