How long will it take 4 people to decorate a house

  • Context: MHB 
  • Thread starter Thread starter gazparkin
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around calculating the time it would take for 4 people to decorate a house, given that 10 people can complete the task in 6 days. The conversation explores different approaches to solving this problem, including concepts of work rate and proportionality.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant presents the initial problem and seeks assistance in determining how long it would take for 4 people to complete the task.
  • Another participant introduces the concept of "people-days," calculating that decorating the house requires 60 people-days, leading to a conclusion that 4 people would take 15 days to finish the task.
  • A subsequent reply reiterates the "people-days" calculation and seeks confirmation on the method used to arrive at the answer.
  • Another participant discusses the inverse proportionality of the number of people to the time taken, suggesting that with fewer people, the time required increases, while noting assumptions about work rates and potential limitations in the scenario.

Areas of Agreement / Disagreement

Participants present differing approaches to the problem, with some agreeing on the calculations involving "people-days," while others emphasize the assumptions and conditions that may affect the outcome. The discussion remains unresolved regarding the implications of varying work rates and the practical limitations of the scenario.

Contextual Notes

Assumptions about the uniformity of work rates among individuals and the nature of the task are not fully explored, which may affect the conclusions drawn from the calculations.

gazparkin
Messages
17
Reaction score
0
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
 
Mathematics news on Phys.org
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!)
 

Similar threads

High School Got these image puzzles at university and couldn't solve half of them
  • · Replies 14 ·
Replies
14
Views
3K
MHB Another work to paint house problem
  • · Replies 3 ·
Replies
3
Views
2K
High School So many people are unable to do simple algebra
  • · Replies 10 ·
Replies
10
Views
2K
MHB Garden Materials Help: Calculate Circumference, Perimeter, Areas & Costs
  • · Replies 1 ·
Replies
1
Views
2K
MHB Rate Problem: How many minutes does it take 14 people to paint 14 walls?
  • · Replies 2 ·
Replies
2
Views
2K
High School Excel: converting a 3-ish week count into a monthly count
  • · Replies 15 ·
Replies
15
Views
2K
MHB How many minutes does it take 14 people to paint 14 walls
  • · Replies 2 ·
Replies
2
Views
7K
MHB Solve exponential equation x^4 = (5x+6)^2
  • · Replies 5 ·
Replies
5
Views
2K
High School Trouble with polynomial long division
  • · Replies 6 ·
Replies
6
Views
2K
MHB Couple of hard trig questions....
  • · Replies 1 ·
Replies
1
Views
2K