SOLUTION: Two teams work in a factory making couches. Team A can make a couch in 3 hours less than team B. Working together, they canmake a couch in 2 hours. How long does it take each te

Question 96230: Two teams work in a factory making couches. Team A can make a couch in 3 hours less than team B. Working together, they canmake a couch in 2 hours. How long does it take each team working alone to make a couch?
Team A:_____________ Team B:___________
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two teams work in a factory making couches. Team A can make a couch in 3 hours less than team B. Working together, they canmake a couch in 2 hours. How long does it take each team working alone to make a couch?
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Team A DATA:
time = x-3 hrs/job : rate = 1/(x-3) job/hr
-------------------
Team B DATA:
time = x hr/job ; rate = 1/x job/hr
-----------------
Together DATA:
time = 2 hrs; rate = 1/2 job/hr
-------------------
EQUATION:
A rate + B rate = together rate
1/(x-3) + 1/x = 1/2
Multiply thru by 2x(x-3) to get:
2x + 2(x-3) = x(x-3)
4x-6 = x^2-3x
x^2-7x+6=0
(x-6)(x-1)=0
x=6 or x=1
------------------
Only x=6 gives positive results for x and x-3
A time to do the job = x-3 = 6-3 = 3 hrs
B time to do the job = x = 6 hrs
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Cheers,
Stan H.

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