Let the average number of vehicles arriving at the gate of an amusement park per minute be equal to k, and let the average number of vehicles admitted by the park attendants be equal to r. then, the average waiting time t (in minutes) for each vehicle arriving at the park is given by the rational function defined by the equation

t(r)= (2r-k) ÷ (2r²- 2kr), where r> k

(a) it is known from experience that on saturday afternoon k= 26. estimate the admittance rate r that is necessary to keep the average waiting time t for each vehicle to 30 sec.

(b) if one park attendant can serve 5.3 vehicles per minute, how many park attendants will be needed to keep the average wait to 30 sec?

Step-by-step explanation:

The given rational function defined by the equation:

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

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

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.

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step-by-step explanation:

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