How would you estimate the total number of cars right now in Highway 101 between San Francisco and Mountain View?

Clarifications and assumptions

1/ We are talking about cars at say 2pm. On a weekday - WED.  Not a holiday and not during summer, spring break or any of those seasonal events. 

Equation

Number of cars on highway = Number of cars entering - number of cars exiting + number of cars on the main highway. 

We can assume cars exiting and cars entering cancel out. 

Cars in main highway = Cars going north from MV to SF + Cars going south from SF to MV. 

Cars going north from MV to SF = Number of exits x avg # of cars between two consecutive exits between MV and SF. 

Number of exits = Distance between MV and SF/ avg distance between 2 exits = 30 miles / 2 miles = 15 exits. 

Its a 4 lane highway. I have typically found traffic to medium at 2pm. 2 cars at a time in 4 lanes. Distance between cars in a lane around 200m. Every 200 meters, we will find 2 cars. Or every 100m, 1 car. Near exits will find 2 more cars.  

Avg # of cars between two consecutive exits = 2 miles = 3.2km/ 100m = 3200/100 = 32 cars + 2 cars near exit = 34 cars. 

15 exits ~ 500 cars. North and South = 500 + 500 = 1000 cars. 

1000 cars seems less. Density is higher near SF. Lets assume each car in the 4 lanes and distance between cars in 100 for ⅓ teh distance from SF to MV. cars in 100m = 4. 1 car every 25m. 

Avg cars between exits = 3200/25 = 130 cars. 

130*5 + 34 *10 = 650 +340 = 1000 cars one way. 

2000 cars both ways.

Note: I'm not familiar with this highway, so it's a little hard for me to estimate whether my answer is within reason. Welcome any feedback. The estimate is much lower than another answer, so I'd love to understand if my answer seems acceptable.

1. CLARIFY: 
   1. What time of day are we using? Assume morning / rush hour. 
   2. Do we consider present day in which COVID has reduced traffic? Yes. 
   3. By cars, should we include all sorts of vehicles including large trucks? Interviewee choice. I choose to include trucks. 
   4. Is it a holiday / special event that would increase traffic significantly more than usual? No.
2. CREATE EQUATION: # of cars on highway = # of cars / mile * total miles * total lanes
3. BREAKDOWN UNKNOWNS:
   1. # of cars / mile 
      1. Length of Cars: There are four major types of cars to consider. We known the average length of a 4 door sedan (most common type of car) is ~ 14.7 ft. 

         1. Car	Length of Car	Feet
            Average 4 Door Sedan	Known variable	14.7 feet
            Average Hatch Back / Station Wagon	1.25 * Sedan	18.4 feet
            Average Van	1.5 * Sedan	22 feet
            Average Large Truck	3 * Sedan	44 feet

            Note: Length of other vehicles is estimated / assumed. 

         2. Length Between Single Cars: Assume that drivers are driving safely and they leave ~16 car lengths between themselves and the next car. 
            1. Sedan to Sedan Length:: If we measure two cars Sedan A to Sedan B, we'd measure as follows: 
               1. Sedan A -- 16 Sedans Length -- Sedan B
                  1. Total Length Between Sedan A and Sedan B: 14.7 * 16 = 235.2 feet
                  2. Total Length Between Sedan A and Sedan B  inclusive of both cars: 14.7 feet + 235.2 feet + 14.7 = 264.6 feet 
            2. Sedan to Average Car Length: 
               1. Let's assume that all cars maintain the same ~235 feet between each other unless the car in front of them is a truck. (Discussed later.)
               2. Let's assume that there are more sedans on the road, but there's a possibility the car in front of them could also be a hatch back or a van (trucks to come later). 
                  1. Average Length of Average Car (i.e. Sedan, Hatch Back or Van): (14.7 + 18.4 + 22) / 3 = ~ 18.4
                  2. Since we assume there are more sedans, let's use the same model as above but replace Sedan B with the average length of Sedan / Hatch Back / Van. Let's call this varaible "Average Car". (These 3 types of vehicles are close enough in length. Trucks are calculated separately because their length is significantly larger.)
                     1. Sedan A -- 16 Sedans Length -- Average Car
                     2. Total Length between Sedan A and Average Car inclusive of both cars: 14.7 feet + 235.2 feet + 18.4 feet = 268.3 feet
            3. Sedan to Truck Length: If a car is driving behind a truck, let's assume they maintain more distance: 300 feet. 
               1. Total Length of Sedan to Truck inclusive of both cars: 14.7 feet + 300 feet + 44 feet = 358.7 feet
      2. Number of Cars in Mile: Let's assume every 30 cars we see a truck. If we are calculating the total length in miles between 30 cars, there are 15 sets to consider (Sedan A -- Safe Driving Distance -- Average Car or Truck) with each set containing 2 vehicles. 14 of these sets will be Sedan to Average Car (i.e 28 vehicles) and 1 set will be Sedan to Truck (i.e. 2 vehicles with one being the truck).
         1. Total Length in 15 Sets of Vehicles (2 vehicles / set): 14 sets will be Sedan to Average Car. 1 set will be Sedan to Truck. 
            1. Total Sedan to Average Car Set Length: 268.3 feet * 14 sets = 3756.2 feet 
            2. Total Sedan to Truck Length: 358.7 feet (calculated above already)
            3. Total Length of 15 Sets of Vehicles: 3756.2 feet + 358.7 feet = ~4115 feet
         2. Total vehicles in 1 mile: Given that 15 sets of vehicles takes approximately 4115 feet, we need to calculate how many additional vehicles we can fit in the remaining space of 1 mile.
            1. 1 Mile = 5280 feet
            2. Leftover Distance in Mile if we only have 15 sets of vehicles: 5280 feet - 4115 feet = 1165 feet
            3. Number of Sedan to Average Car Sets in Leftover Distance: 1165 / 268.3 = ~ 4 additional Sedan to Average Car sets (i.e. 8 more cars since each set has 2 cars) 
            4. Total Number of Any Vehicles in 1 Mile: 30 vehicles (i.e. from original set of 15) + 8 (i.e. additional cars) = 38 vehicles (assuming the mile is completely used / spread out)
   2. # of Miles: Highway 101 from SF to Mountain View is ~38 Miles.
   3. # of Lanes: Highway 101 has 8 lanes of cars. 
4. TOTAL NUMBER OF CARS: 
   1. If we assume Highway 101 is completely full with vehicles spread as stated above, 38 vehicles / mile * 38 miles * 8 lanes = 11,552 vehicles
   2. Given morning rush hour in COVID, we assume while the highway is busy, it's not as busy as it was previously. Assume 70% occupancy. 
      1. .7 * 11,552 = 8086 vehicles during morning rush during COVID
   3. Note, if it were not COVID, I'd assume that morning rush hour makes the highway much busier and perhaps occupancy is at 125% or even 150%. 
   4. Assumption: Cars are entering the highway at a steady pace as they leave it.