Final answer:
Average queue length: 6 cars, Average time: 10 minutes. (Option b is the correct answer).
Step-by-step explanation:
To determine the average queue length and the average time a car is in the system, we can use queuing theory formulas. The average queue length (L) can be calculated using the formula: L=λ⋅W
where
λ is the arrival rate and
W is the average time a car spends in the system.
The arrival rate (λ) is given by the inverse of the service time, which is 1/10 cars per minute. So, λ=1/10 cars/minute.
Now, let's consider the options:
Option a: L=10×6=60 cars, which is not correct.
Option b: L=1/10×10=1 car, and W=10 minutes. Thus, L=1×10=10 cars, which is correct.
Option c: L=1/10×12=1.2 cars, which is not correct.
Option d: L=1/10×5=0.5 cars, which is not correct.
So, option b is the correct answer with an average queue length of 6 cars and an average time of 10 minutes.
So, option b is the correct answer with an average queue length of 6 cars and an average time of 10 minutes.
Option b provides the most accurate representation of the system, with an average queue length of 6 cars and an average time of 10 minutes, reflecting a realistic scenario for the Petroco service station.