Vehicles arrive at a recreational park booth at a uniform deterministic rate of 5 veh/min. If uniform deterministic processing of vehicles (collecting of fees) begins 20 minutes after the first arrival and the total delay is 3200 veh/min, how long after the arrival of the first vehicle will it take for the queue to be cleared?

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Answer:

The right solution is "32 min".

Explanation:

The given values are:

Total delay,

= 3200 veh/min

Deterministic rate,

= 5 veh/min

For 1st arrival, time taken

= 20 minutes

Now,

To be clear the queue, the time take will be:

= [tex]\frac{Total \ delay}{Deterministic \ rate\times (1st \ arrival \ time \ taken)}[/tex]

On substituting the values in the above formula, we get

= [tex]\frac{3200}{5\times 20} \ min[/tex]

= [tex]\frac{3200}{100}[/tex]

= [tex]32 \ min[/tex]

Based on the information given, the timer taken for the queue to be cleared will be 32 minutes.

Calculation of the time taken

Based on the information given, the time taken will be calculated as:

= Total delay / (Deterministic rate × 1st arrival time)

= 3200 / (5 × 20)

= 3200 / 100

= 32 minutes

In conclusion, the correct option is 32 minutes.

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