SOLUTION: If a wall was built by 4 men and 2 women in 5 days how many days it will take to built by 3 men and 1 women?

Question 568937: If a wall was built by 4 men and 2 women in 5 days
how many days it will take to built by 3 men and 1 women?
Found 2 solutions by bucky, Theo:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Lacking further information to the contrary, you can assume that the men and the women have the same working ability. That being the case, the fact that each team is a mixture of men and women has no bearing on this problem. Just count the number of persons on the two teams. Doing this changes the problem to: If a wall was built by 6 persons in 5 days, how many days will it take for 4 persons?
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That being the case, you can do the problem by determining the number of person-days it takes to build the wall. Do that by multiplying the persons on a team times the number of days it takes. You are told that 6 people can build the wall in 5 days and by multiplying 6 times 5 you can see that it takes 30 person-days to finish the job.
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The other team consists of 4 persons. In order to put in the 30 person-days needed to build the wall 4 persons will need to work 7.5 days (30 divided by 4).
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That seems about correct because if 6 people take 5 days to complete the wall, using less people on a team will certainly mean that more than 5 days will be needed to complete the wall. In fact, the ratio of 6 persons to 4 persons tells you how much longer. 6 is to 4 can be reduced to 3 is to 2. So it will take 3/2 times 5 days to complete the job with the smaller team, and 3/2 times 5 days equals 15/2 days which reduces to 7.5 days, the same answer as we previously determined by using person-days.
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I hope this analytic approach to the problem gives you a better understanding of the procedures that can be used to solve it. Understanding math and using a thought process that applies to the problem is more important than looking for an equation that you can just substitute numbers into to get some sort of an answer, whether it is reasonable or not.
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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you don't provide any information about how fast each is working, so the assumption is that they all work at the same rate.

if the wall is built by 4 men and 2 women in 5 days, then you calculate their rate of work (how fast they work and their rate of work are used to talk about the same thing) as follows:

rate * time = units of work.
the number of units is 1 (the wall).
the rate that they work is x (we don't know it yet).
the time is 5 days.
we get rate * time = units of work equation becomes:
x * 5 = 1
we divide both sides of the equation by 5 to get:
x = 1/5
the 4 men and 2 women, all working together, have a speed or rate of work that is equivalent to building 1/5 of the wall per day.
if you divide the rate by the number of people, then you get:
1/5 divided by 6 = 1/5 * 1/67 = 1/30.
this means that each person builds 1/30 of the wall per day.
confirm your equation by going back to the original problem.
rate * time = units of work.
the units of work is equal to 1 (the wall).
the rate per person is 1/30 of the wall per day.
the number of people is 6.
the equation becomes:
6 * 1/30 * time = 1
this becomes:
6/30 * time = 1
multiply both sides of this equation by 30/6 to get:
time = 30/6 * 1 which becomes:
time = 5 days.

the equation works with the original situation.
now reduce the number of men and women to 4.

the equation becomes:
4 * 1/30 * time = 1 which becomes 4/30 * time = 1
multiply both sides of this equation by 30/4 to get:
time = 30/4 which becomes:
time = 7.5 days.

all of this assumes that each person is working at the same rate of 1/30 of the wall per day.
there is no distinction between the rate that men work and the rate that women work, nor is there any distinction between the rate that individual people who are different from each other work.

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