An automatic car wash with a single bay takes a constant 3 minutes to wash.The arrival rate is 10 cars per hour.Determine the average time a car spends in the system.The arrival rate of cars tends to follow a Poisson distribution.
A)5 minutes
B)6 minutes
C)3.5 minutes
D)4.5 minutes

Question

Quizplus · Accepted Answer

The average time a car spends in the system can be calculated by adding the time spent waiting in the queue and the time spent being washed.

Since the arrival rate follows a Poisson distribution, we can assume that the interarrival time of cars follows an exponential distribution with a mean of 6 minutes (since there are 10 cars arriving per hour).

The average time a car spends waiting in the queue can be calculated using Little's Law: 
L = λW, where L = average number of cars in the system, λ = arrival rate, and W = average waiting time in the queue. 
Since there is only one bay, the number of cars in the system is equal to the number of cars waiting in the queue. So, 
W = L/λ = 1/10 = 0.1 hour = 6 minutes.

Therefore, the average time a car spends in the system = 6 + 3 = 9 minutes. Hence, the best choice is D (4.5 minutes is not the correct answer).

An Automatic Car Wash with a Single Bay Takes a Constant