Problema Solution
After a performance at a county fair, security guards have found that the grandstand area can be emptied in 8 minutes if both the east and west exits are opened. If just the east exit is used, it takes 6 minutes longer to clear the grandstand than it does if just the west exit is opened. How long does it take to clear the grandstand if everyone must file through the east exit?
------------minutes
Answer provided by our tutors
Let x be the number of hours taken only by west exit. Then
(x+6) is the time in minutes taken by east exit.
x(x+6)/(x+x+6)=8.
(x^2+6x)/(2x+6)=8.
(x^2+6x)=8(2x+6).
x^2+6x-16x-48=0.
x^2-10-48=0.
By solving quadratic x=13.54 minutes.
It takes (13.54+6)=19.54
minutes to lear the grandstand if everyone must file through the east exit.