Consider a very long section of highway consisting of a travel lane and an adjacent passing lane. Traffic in the subject direction is stationary and an aerial photograph shows that 1/5 of the vehicles in the highway section are trucks and that 4/5 are cars. The cars and trucks travel at constant speeds of 50 mph and 40 mph, respectively. Cars can pass trucks with negligible delay. Consider the following three scenarios. a) There is a sudden snow storm after which the cars can no longer pass the trucks. The cars catch-up with the trucks and follow in quene.
b) The section of highway with free passing feeds into a long section of road on which passing is impossible, but all vehicles can enter the no-passing section without delay. Within the no-passing zone, the cars catch-up with the trucks and follow in queue.
c) The passing zone lane is actually an empty lane normally reserved for opposing traffic. Suddenly, a long stream of vehicles appears in the opposing lane traveling at 40 mph (in the opposing direction). This opposing traffic stream prevents vehicles from passing so that cars (in the subject direction) queue behind trucks.
For each of the above scenarios, after the cars have joined the queues, what is the average number of cars queued behind each truck?