How many cars are on 101 between San Francisco and Mountain View?

Question

How many cars are on 101 between San Francisco and Mountain View?

Asked at Google over a year ago

1.9k views

Estimation category

Asked at

1.9k views

How to answer Estimation questions

Interview Guide

Top Estimation interview questions

Calculate the number of queries answered by Google per second.45 answers | 78.5k views
How many dentists are there in New York?33 answers | 36.7k views
Estimate the number of Uber rides.30 answers | 51.3k views
See Estimation PM Interview Questions

Invite members
Invite by email

Add another

PM Team · Answer 1 · 2018-08-08T02:07:50+0000

It takes 1 hour to drive from mountain view to san Francisco at about 70 miles per hour. So the distance between mountain view and san francisco is 1 hour x 70 miles / hour = 70 miles.

I have noticed that cars are usually 100 feet away from other on average when there is no traffic. Assuming there is no traffic in the highway now and all cars in the highway are keeping a 100 feet distance from each other, the number of cars per lane would be 100 miles / 100 feet. Given 1 mile is equal to ~ 5300 feet, we can assume the total number of cars per lane is 100 miles x 5300 feet per mile / 100 feet = 5300. There are about 10 lanes (5 southbound, 5 northbound) at any point in the road. Assuming all roads are equally occupied, total number of cars will be 5,300 x 10 = 53,000. Of course this number changes depending on the time of the day. As traffic increases, the distance between cars will reduce and number of cars per lane increases. At certain times of the day, traffic might be high on one side of the highway. In those situations, we will have to calculate the number of cars per side separately.

anonymous · Answer 2 · 2021-08-27T20:09:30+0000

Assumptions :

Only cars (Small, medium, Large sized) taken into consideration, Medium sized for ease of calculation
Gap between 2 cars : 10 feet
Non COVID, Average day time traffic

What we know :

Medium size cars : 15 feet in size
Distance between MTV and SFO = 33 miles ~ 35 miles
8 lane roads, 4 lane roads, Average 6 lane roads

Top line Equation:

Total distance / (Car size in feet + gaps )

1 mile = 5000 ft (Approx)

MTV-> SF = 35 miles = 175000 ft

Single use case :

One car (15 ft) + gap behind (10 ft)= 25 ft

One 100 ft road is covered with 4 cars

Extrapolation :

100 ft -> 4 cars (In the top line Equation),

175000 ft -> (175000*4)/100 = 7000 cars

One lane = 7000 cars

Total of 6 lanes ( 3 lanes to and 3 lanes fro) , measuring only from MTV=> SFO, so 3 lanes = 7000 *3 lanes = 21000 cars

Dividing equally across 3 lanes = 7000 cars per lane

1 lane is Fast track (assuming) , less number of cars 50% = Approx 17000 cars in total

Looks to be a higher number!!!

1. MTV => SFO, train services available, 30% of ppl take trains

2. Gaps between 2 cars is more than 10 feet considering fast moving cars.

3. There are car ride sharing, assuming traffic is nominal.

Recalculating,

30% deduction (including #1,#2, #3) = ~ 12 k cars on a normal day plying in the morning time.

@Nag · Answer 3 · 2021-08-15T04:03:40+0000

Alternative:

SFO to Mountain View is about 20 miles, 8 laned highway( 4 on each side)

Assumption 25% of vehicles on road will be cars, 30% SUVs, 20% pickup trucks, 15% large trucks and 10% Semis -->a

Length of vehicles including buffer between 2 vehicles

cars= 21 ft, SUV=25 ft, Pickup-30 ft, Large truck=40 ft, Semi-120ft-->b

lets say number of cars is x then number of suvs will be 30/25 x, pickups will be 20/25x, large trucks will be 15/25x, semis will be 10/25x

Thus in a mile of highway or 5280 feet,

21ft * x+25ft *30/25x + 30ft * 20/25x + 40ft * 15/25x + 120ft * 10/25x = 5280

147x=5280

x=36 or there will be 36 cars in a single lane of a 1 mile highway.

SFO to MTV will be 20 miles of 8 laned highway( 4 on each side)

Cars will be 36*20*8= 5760 cars.