Estimate the number of gas stations in SF city.

Average Capacity of 1 gas station: 12000 -25000 gallons = 18000 gallons ( whenever i go to a gas station there are 4-5 cars. So assuming in an hour 20 cars are served ( peak will be more and night will be less, so around 500 cars served in day, and average car/Big vehicle tank capacity will be 25 -50 gallons. As a gas station generally gets filled once in a day assuming capacity will be : 12000-25000 gallons .

Value: 100 M/20000 *30 days =100 * 10/6 = 170

Sanity Check

No of Gas station: : SFO area/No of gas station per square Km

SF Area: 120 Square Km,

Let’s say approx every 1 square km has 1 gas station. So there should be 120 gas station

This is in the same range , so it should have around 120-170 gas stations.

Ans: 150 Gas station ( Keeping average)

Satish Nandi · Answer 2 · 2021-04-02T08:00:53+0000

S

Satish Nandi

Platinum PM

Apr 2, 2021

You have to consider the ratio of car to population should be much lower in the city. So likely it is 1 Car for 10-15 people. For simplicity lets assume it is 100,000 cars. Most city dweller do not use their cars, so it will be half of 100K, but lets add 100k cars (needing gas) driving into the city. Effectively 150K cars in the city.

150K * 15 gallon/car = 2250K gallons for every 2 weeks or ~75k gallon per day. That is 5000 cars per day needing gas in the city. Mostly daytime, if gas stations fuels 10 cars/hour, it is 120-140 cars per day.

5000 cars/140 per station = 35-40 gas stations.

It is still on the higher side. I was expecting around 30ish.

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Eli Marcus

Platinum PM

Apr 2, 2021

@snandi I wouldn't have passed you to the next round based on your anwers. I would expect a more compelte answer like the one I demoed bleow - following the steps of a framework. I highlighted the steps of the framwork in bold and solved the equation for fun. FYI: Based on a google search there are more gas stations than you think in SF- I think the right answer is closer to 100. Having lived in SF I would have thought your low number was right . Please note that in an estimation question getting the answer right isn’t that important. Your process is important.

How I would have done the question

Ask Clarifying Questions - I assume you mean consumer gas stations and not include private fleet gas stations? Can I assume when you say SF you mean SF and not the bay area?
Create an equation - tell the interviewer how you plan to solve the problem.
1. I am going to determine the number of cars in SF on any given day * the % of cars that need gas / the number of cars a gas station serves = number of gas stations.
Tell the interviewer how you got to your assumptions - below I get to estimated numbers using sub equations
1. how did you get 100K cars? - I would have gotten to the number of cars like -
  1. Population of San Francisco = 900,000 - Round up to 1,000,000 (its an estimation)
  2. Household size 2.5 = 1,000,000/2.5 = 400,000 households
  3. Many households in SF don’t have a car and rely on public transportation so we can make an assumption that the average household has 2 cars but in a city like SF that number will be lower so say 1 car or we can take your number even lower ~ like ½ car per household. 400,000 households *.5 = 200,000 cars.
  4. SF has a big in bound commute - something like 250,000 (I lived there, but I also cheated and looked up the number). Now a lot of people take public transportation but the bridges are packed - I really don’t know but let's assume that ¼ drive in = 60,000 (note the estimation).
  5. Total cars in SF per day = 260,000
2. The average driver fills up every 1 or 2 weeks so I’ll average it at 1.5
  1. 7 days a week * 1.5 = days per fill up = 10 (rounded estimation)
  2. 260,000 cars / 10 days between fill ups = 26,000 cars per day need a fill up
3. Cars serviced by a gas station
  1. 3 islands with 3 pumps each
  2. 10 min per fill up - pay, pump, leave (based on personal expereince filling up my car)
  3. At peak a station can service 3*3*6 rotations per hour 54 cars per hour at peak (50 for estimation purposes)
  4. Gas stations are not a peak a lot of the time - the following chart is a good faith estimate of fill rate by hour
    1. 4am 10% = 5
    2. 5am 20% = 10
    3. 6am 50% = 25
    4. 7am 100% = 50
    5. 8 am 100% = 50
    6. 9 am = 70% = 35
    7. 10am = 20% =10
    8. 11 40% = 20
    9. 12 60% = 30
    10. 1 60%= 30
    11. 2 40% = 20
    12. 3 30% = 15
    13. 4 70% = 35
    14. 5 100% = 50
    15. 6 100% = 50
    16. 7 70% = 35
    17. 8 50% = 25
    18. 9 20% 10
    19. 10 20% 10
    20. 11 10% 5
    21. 12 10% 5
    22. 1 10% 5
    23. 530 per day

Calculate the number 26,000 / 500(round for easier math) = 52

Do a sanity Check
1. 52 seems low. If I were going to tweak the equation I would adjust the cars per household in SF and maybe look at the days between fill ups. Drivers that stay in the city don’t drive far but have to deal with traffic and hills - likely driving down mpg and drivers that commute drive more and fill up often.
  1. 400,000 households *.75 cars per household = 300,000 + 60,000 for commuting = 360,000
  2. If they fill up once a week then 7 days between fill ups
    1. 360,000 / 7 50,000 fill ups per day
      1. 50,000 / 500 cars per station = 100 stations
Summary and list limitations
1. Our equation was number of cars in SF per day / days between fills / fills per station
  1. Our original equations was 260,000 /10 /500 = ~52
  2. Our sanity check equation was 360,000 / 7 /500 = ~100
  3. If we treat these as bounds then I would assume the number of gas stations in SF is at the low end 52 and at the high end 100
  4. Limation - It is worth noting that I didn't account for the fact that some SF drivers fill up outside of SF and some commuters do as well.
  5. Limitation - I didn't account for electric cars which in SF is a higher percent than other geo's

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prashney · Answer 3 · 2021-02-10T06:48:03+0000

Depends on

Total population density
Travel habits of the people. Miles per day
Mileage per vehicle - take terrain into account. 10 miles a gallon
% gas vehicles = 80%
% people driving cars = 60%

population density = total population / total area = 1M / 100sqmiles = 10k

# gas vehicles per sq mile = population density * % driving cars * % gas vehicles = 10k * 0.6 * 0.8

Gas used per sq mile = # gas vehicles per sq mile * miles per day per vehicle / avg mileage.

= (10k * 0.6 * 0.8) * 20 / 10 = 10k gallons

#GS per sq mile = gas used / capacity per station = 10k / 10K = 1

#GS = GS per sq mile * total area = 1*100 = 100

stashbag · Answer 4 · 2021-01-12T02:27:47+0000

Gas Stations = Refueling trips / Refueling capacity per station

High level approach (SWAG)

Area of SF city = 7 miles * 7 miles —> ~50 square miles.
- Area served by a gas station 2 sq miles (based on observation)
- Total Gas stations = 50/2 = ~25

Bottom up approach

Residents in SF = 800K
Households = (800/3) —> 300K
- Cars = 450K (1.5 per HH)
Gas stations
- Avg # fueling pumps per station = ~6
- Avg refueling time/car = 6 mins —> 10 cars an hour per pump
- Per hour capacity = 60 cars per hour per station
- Hours open / day = 16 hrs
- Daily max capacity = 16*60 = ~960 —> 1000 refuels per day per station
- Monthly capacity = 30000 refuels
Cars refueling
- Avg refueling needs = 2x per month
- Total refueling = 450*2x = 900K refuels per month
- Refueling out of city = 10%
- Refueling in city = ~800K

Gas Stations = Refueling trips / Refueling capacity per station —> 800,000 / 30000 = ~26 gas stations

Things to watch out for

Assumption of number of refuels is highly sensitive to where people work and refuel.
Commuters coming into the city may be using SF based gas stations but difficult to model that