SOLUTION: If the east west exit doors of a banquet hall are open, the occupants can clear out in two minutes. It takes 3 minutes longer to clear the hall if just the east door is open as it

Algebra ->  Test -> SOLUTION: If the east west exit doors of a banquet hall are open, the occupants can clear out in two minutes. It takes 3 minutes longer to clear the hall if just the east door is open as it       Log On


   

Question 439046: If the east west exit doors of a banquet hall are open, the occupants can clear out in two minutes. It takes 3 minutes longer to clear the hall if just the east door is open as it does if just the west door is open. How long does it take to clear the hall if just the west door is open? I got 3 but then I added it to x+3 to get 6 not sure if it is correct.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If the east and west exit doors of a banquet hall are open, the occupants can clear out in two minutes. It takes 3 minutes longer to clear the hall if just the east door is open as it does if just the west door is open. How long does it take to clear the hall if just the west door is open? I got 3 but then I added it to x+3 to get 6 not sure if it is correct.
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together rate = 1/2 job/min
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west-door rate = 1/x job/min
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east-door rate = 1/(x+3) job/min
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Equation:
rate + rate = together rate
1/x + 1/(x+3) = 1/2
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Multiply thru by 2x(x+3) to get:
2(x+3) + 2x = x(x+3)
2x+6 +2x = x^2+3x
x^2-x-6 = 0
Factor:
(x-3)(x+2) = 0
Positive solution:
x = 3 minutes (time to clear the room if only west door is open)
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x+3 = 6 minutes (time to clear the room if only east door is open)
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Cheers,
Stan H.