SOLUTION: Two teams working together can complete the project in 45 days. Team A works for 18 days and team B works for 12 days and they complete 30% of the project. How long will each team

Question 352056: Two teams working together can complete the project in 45 days. Team A works for 18 days and team B works for 12 days and they complete 30% of the project. How long will each team take to complete the project when they work alone.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Team A working alone to complete the project
Then Team A works at the rate of 1/x of the project per day
And let y=amount of time it takes Team B working alone to complete the project
Then Team B works at the rate of 1/y of the project per day
Were are told that together the two teams can complete the project in 45 days
Then, together the two teams work at the rate of 1/45 of the project per day.
Soooo, our first equation is:
1/x + 1/y=1/45-----------------------------eq1
In 18 days, Team A completes (1/x)*18=18/x of the project
In 12 days team B completes (1/y)*12=12/y of the project
And we are told that this work completes 30% of the project.
Soooo, our second equation is:
18/x +12/y=0.3*1 (1 project, that is)--------eq2

Multiply eq1 by 12 and then subtract it from eq2 and we get:
6/x =0.03
0.03x=6
x=200 days---time it takes team A working alone
substitute x=200 into eq1 and we get:
1/200+1/y=1/45 multiply each term by 200y
y+200=4.44y
3.44y=200
y=58.1 days ---time it takes team B working alone
CK
(1/200)*45 +(1/58.1)*45=1 (project, that is)
0.225 + 0.775=1
~~~~~~1=1
Hope this helps---ptaylor
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