Can anyone help me solve this problem?

Question

According to a Scientific American article (May, 1990), current freeways can sustain about 2380 vehicles per lane per hour in smooth traffic flow at speed 96 km/h. Above that figure the traffic flow becomes "turbulent" (stop-and-go).

a. If a vehicle is of length 4.5 m on the average, what is the average spacing between vehicles at the above traffic density?

b. Collision-avoidance automated control systems, which operate by bouncing radar or sonar signals off surrounding vehicles and then accelerate or brake the car when necessary, could greatly reduce the required spacing between vehicles. If the average spacing is a distance 9.3 m, how many vehicles per hour can a lane of traffic carry at speed 96 km/h?

Answer 1

PART A:

A car traveling 96 km/h will cover 96 km in 1 hour.  That is 96,000 meters.  Dividing that by 2380 vehicles you have 40.3 m per vehicle (including the vehicle and space behind).

Subtracting the 4.5m occupied by the vehicle, you get the spacing between each vehicle.

Answer:

An average of 35.8 m spacing between each vehicle.

PART B:

Adding 9.3m to 4.5m gives 13.8 m per vehicle (and space).  Dividing that back into the 96,000 m of distance in an hour you have:

96,000 / 13.8 = 6956.52

Answer:

About 6,956 vehicles