MHB How long will it take 4 people to decorate a house

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It takes 10 people 6 days to decorate a house, equating to 60 people-days for the entire job. Therefore, if only 4 people are working, the time required to complete the task is calculated by dividing the total people-days by the number of workers, resulting in 15 days. The discussion highlights the concept of "people-days" and how the number of workers inversely affects the time needed to finish the job. It is noted that this calculation assumes all workers contribute equally and efficiently. If tasks require specific physical capabilities, the time may vary significantly.
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There may be a simple way of answering this but I'm stumped! it takes 10 people 6 days to decorate a house. how long will it take 4 people?

Any help appreciated
 
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Ever heard the term "man-hours" to complete a job? This is very similar in units, except it's "people-days" ...

1 house decorated by 10 people in 6 days means it takes 60 people-days (same as 60 days for 1 person to finish decorating the house)

(60 people-days to finish a house)/(4 people working) = 15 days to finish
 
skeeter said:
Ever heard the term "man-hours" to complete a job? This is very similar in units, except it's "people-days" ...

1 house decorated by 10 people in 6 days means it takes 60 people-days (same as 60 days for 1 person to finish decorating the house)

(60 people-days to finish a house)/(4 people working) = 15 days to finish

Thanks for this Skeeter. So the calculation is people X days (in the original calculation) then divide by however number of people are in the question?
 
The more people you have the less time it will take. This is an "inverse" proportion. You have 4/10= 2/5 as many people so it will take 10/4= 5/2 as long.

(Also, this is assuming that each person works at the same rate no matter how many people there are. If "decorating" involved lifting some object so heavy it takes 5 people to lift it, 4 could never finish!)
 

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