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

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) (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.
-----
together rate = 1/2 job/min
---
west-door rate = 1/x job/min
----
east-door rate = 1/(x+3) job/min
====================================
Equation:
rate + rate = together rate
1/x + 1/(x+3) = 1/2
---
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)
---
x+3 = 6 minutes (time to clear the room if only east door is open)
==================================================================
Cheers,
Stan H.
RELATED QUESTIONS
If there are a total of 5 doors, then how many ways can a student enter the hall by one... (answered by Fombitz)

Dear tutor please help!! If it takes 52 minutes to clear a full stadium when 8 gates... (answered by Boreal)

A snowplow company has two trucks. One truck has a large plow in the front and can clear... (answered by vleith)

Four Managers are attending a safety conference that starts in 21 minutes. The conference (answered by vleith)

One pipe can fill a tank in 45 minutes and another pipe can fill it in 30 minutes. if... (answered by ramkikk66)

An office building has 7 doors. Four doors are only entrances to the building and two... (answered by stanbon)

The Austin Healthmate 400 can purify the air in a conference hall in 15 fewer minutes... (answered by josmiceli)

A water tank has two valves, A and B. When only valve A is open, the tank is emptied in... (answered by lwsshak3)

a sink can be filled from the faucet in 5 minutes. it takes only 3 minutes to empty the... (answered by greenestamps)