Respuesta :
Step-by-step explanation:
The given rational function defined by the equation:
[tex]T(r)=\frac{(2r-k)}{(2r^2- 2kr)}[/tex]
where :k = average number of vehicles arriving at the gate per minute
r = average number of vehicles admitted by the park attendants
T = the average waiting time in minutes for each vehicle
a) k = 26 , r = ?, T = 30 seconds
T(r) = 30 seconds
[tex]30=\frac{(2r-30)}{(2r^2- 2\times 30r)}[/tex]
[tex]60r^2-1800r=2r-30[/tex]
[tex]60r^2-1802r+30=0[/tex]
on solving:
r = 0.016657 , 30.017
r = 30.017 (accept, given that r > k )
Admittance rate r that is necessary to keep the average waiting time T for each vehicle to 30 sec is 30.017.
b) k = 5.3, r = ?, T = 30 seconds
T(r) = 30 seconds
[tex]30=\frac{(2r-5.3)}{(2r^2- 2\times 5.3r)}[/tex]
[tex]60r^2-318r=2r-5.3[/tex]
[tex]60r^2-318r-2r+5.3=0[/tex]
[tex]60r^2-320r+5.3=0[/tex]
r = 0.016657 , 5.31672
r = 5.31672 (accept, given that r > k )
5.31672 park attendants will be needed to keep the average wait to 30 seconds.
