A toll booth on a turnpike is open from 8:00 AM until midnight. Vehicles start arriving at 7:45 AM at a uniform rate of 6 veh/min. At 8:15 AM the rate drops to 2 veh/min. If vehicles are processed at a uniform rate of 6 veh/min, determine when the queue will end, the total delay, the maximum queue length, and the longest vehicle delay.

The vehicles start arriving at 7:45 AM at a rate of 6 veh/min.

then, until the 8:00 AM that the vehicles start being processed, the amount of vehicles accumulated is 6veh/min*15min = 6*15 vehicles = 90 vehicles.

At 8:00 am, when the vehicles start to being processed, we have a queue of 90 vehicles, and at this point, each minute 6 vehicles arrive and also 6 vehicles are processed, so the queue does not change.

At 8:15 AM, the rate at which the vehicles arrive is equal to 2 veh/min.

then, from this hour we have that the number of vehicles in the queue can be described by the equation:

V (t) = 90 + 2*t - 6*t

where t is the number of minutes that passed since the 8:15 AM

this means: we have an initial number of 90 vehicles, and every minute 2 new arrive and 6 are processed.

The queue will end when we have that V(t) = 0

this is:

90 - 4t = 0

t = 90/4 = 22.5 mins.

This means that the queue will end at:

8:15 am + 22.5mins = 8:37.5 Am

You also ask for the longest delay, I guess this is how much a vehicle must wait until it is processed.

knowing that 6 vehicles are processed per minute, the car in the last place (car number 90) must wait 15 minutes, because of 6*15 = 90

so the longest delay is 15 mins.

and this is the same for the first car that arrives at 7:45 AM, this car also needs to wait for 15 minutes.

answer: its c lololo

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation: