Problema Solution
If the east and west exit doors of a banquet hall are open, the occupants can clear out in 2 minutes. It takes 3 minutes longer to clear the hall if just the east door is open than 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?
Answer provided by our tutors
Let
x = the minutes needed for the hall to clear when the west door is open, this means that in 1 minute 1/x of the hall will clear.
x + 3 = the minutes needed for the hall to clear when the east door is open, this means that in 1 minute 1/(x + 3) of the hall will clear.
If both doors are open in 1 minute 1/2 of the hall will clear.
Now we can write:
1/x + 1/(x + 3) = 1/2
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click here to see the equation solved for x
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x = 3 min
We need to ignore the negative solution since the time can not be negative.
The hall will clear in 3 minutes if only the wast door is open.