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

[gazparkin]

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

 

[skeeter]

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

 

[gazparkin]

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?

 

[HallsofIvy]

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!)