SOLUTION: two teams of construction workers had to renovate for 12 days. after 8 days during which the two teams worked together, the first team was assigned a different job. the second tea

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Question 1095920: two teams of construction workers had to renovate for 12 days. after 8 days during which the two teams worked together, the first team was assigned a different job. the second team continued to work for 7 more days until the renovation was complete. how long did will it take each team to renovate if they werent working together?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Team1 does one job in x days.
Team2 does one job in y days.
Description would give .

Might be easier if give different variable to 1%2Fx and to 1%2Fy, and then treat the system as two linear equations.

system%28p=1%2Fx%2Cr=1%2Fy%29

system%28%28p%2Br%29=1%2F12%2Cand%2C%28p%2Br%29%2A8%2B7r=1%29

system%2812p%2B12r=1%2C8p%2B8r%2B7r=1%29

system%2812p%2B12r=1%2C8p%2B15r=1%29------solve this linear system for p and r.

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I have not checked these results yet but solution found is highlight_green%28x=28%29 and highlight_green%28y=21%29.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
In 8 days that two teams worked together, they completed 2%2F3 of the job (since the entire job was scheduled for 12 days).


Thus only 1%2F3 of the job was remained, and it was done by the second team in 7 days.


Hence, it would take 3*7 = 21 days for the second team to renovate if the first team  does not participate.


Thus the combined rate of work of the two teams is 1%2F12 of the job per day,
while the rate of work of the second team is 1%2F21 per day.


It implies that the rate of work of the first team is the difference 1%2F12-1%2F21 = 21%2F%2812%2A21%29+-+12%2F%2812%2A21%29 = 9%2F%2812%2A21%29 = 1%2F%284%2A7%29 = 1%2F28.


Hence, it would take 28 days for the first team to renovate if the second team  does not participate.

Answer. 28 days for the first team and 21 days for the second team.


Lesson to learn from this solution. 

    You do not need solve any equations to get the answer.

    What you really need  is  a) to know what the rate of work is;
                              b) to read the condition attentively, and
                              c) to think 1 - 2 minutes before to start writing.


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It is a typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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And the last notice:

        writing by @josgarithmetic is not adequate for this problem.

        So,  for your safety,  it is better to ignore it.


Actually,  this problem is for  5-6  grade students,  who didn't learn system of equations yet.