SOLUTION: A team of 4 people has just finished half of a project in 10 days. If the rest of the project needs to be done in 5 more days, how many more people are needed?

Question 357297: A team of 4 people has just finished half of a project in 10 days. If the rest of the project needs to be done in 5 more days, how many more people are needed?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the assumption is that they all work at the same rate.

right off the bat, i would say 8 people would be required.

that's because twice as many people should be able to do the same work in half the time assuming that they all work at the same rate.

a more formal approach would be as follows;

Rate * Time = Units

The number of units is equal to 1 (the project).

Since half the project was finished, then Units = .5

Since the time it took was 10 days, then Time = 10

The formula becomes Rate * 10 = .5

Divide both sides of this equation by 10 to get Rate = .5/10 which becomes:

Rate = .05 units per day.

This means that 4 people work at the the rate of .05 of the project per day.

10 * .05 = .5 which means that in 10 days 4 people finished half the project.

if you divide the rate of 4 people by 4, then you get the rate of 1 person.

the rate of 1 person becomes .05/4 = .125 of the project per day.

The question is how many people are required to finish the project in another 5 days.

the same formula applies.

rate * time = units

number of units = .5 (the other half of the project)
time = 5 (the number of days required to finish the project).

the formula becomes:

rate * 5 = .5

divide both sides of the equation by 5 to get:

rate = .5/5 = .1

this means that .1 of the project needs to finished each day.

the rate of each person is .125 of the project per day.

multiply that by 8 and you get .1 of the project per day because 8 * .125 = 1.

8 persons are required to finished the project in another 5 days.

the combined rate of the people is additive.

if 1 person can do 1/2 of the project in one day and another person can do 1/2 of the project in 1 day, then both people will be able to complete the project in 1 day. each person working alone would take 2 days.

same concept applies to this problem.

each person can finish .125 of the project in one day.
8 persons can finish .1 of the project in one day.
5 days total are required.

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