1. Dashboard 1
  2. Consulting Q&A 2
  3. How many trains are there on the Paris Underground 3
1

How many trains are there on the Paris Underground

brain teaser guess-estimates

Can someone help to answer this type of question:

That's how I would approach this problem:

1. #trains = #line multiply by #train per line

2. #train per line= frequency of train (how long I wait at a given station) multiply by average time between two station

Assumptions:

- Let's say that during peak hours I have to wait maximum 3 minutes at a given station to have a train and that the length of time between two station is 1min30

- there is 14 lines in Paris and on average 21 stations per line

________

if I must wait 3 minutes to get a train it means that there is one train every three stations at a given time (so 21/3= 7 trains per line)

As there is two ways in a line we must double it to 14 trains per line

Finally there is 14 lines so we must multiply 14 by 14 which gives me 196 trains

By doing some research I found out that this number is relatively low (approximately 500 trains during peak hours)

How would you approach this problem?

Thanks for your help

Can someone help to answer this type of question:

That's how I would approach this problem:

1. #trains = #line multiply by #train per line

2. #train per line= frequency of train (how long I wait at a given station) multiply by average time between two station

Assumptions:

- Let's say that during peak hours I have to wait maximum 3 minutes at a given station to have a train and that the length of time between two station is 1min30

- there is 14 lines in Paris and on average 21 stations per line

________

if I must wait 3 minutes to get a train it means that there is one train every three stations at a given time (so 21/3= 7 trains per line)

As there is two ways in a line we must double it to 14 trains per line

Finally there is 14 lines so we must multiply 14 by 14 which gives me 196 trains

By doing some research I found out that this number is relatively low (approximately 500 trains during peak hours)

How would you approach this problem?

Thanks for your help

 Recent activity on Oct 01, 2017
4.2 k Views
1 answer
  • Upvotes
  • Date ascending
  • Date descending
Best Answer

Hey,

I am new to this too, but I think I have some ideas for your problem.

Your approach looks good, but I think you have a mistake in how you time the trains. You say that there is one train every three stations and that it takes 1m30s to travel the distance from one station to the next. But how long does the train spend at each station?

My approach would be to represent each line as a timeline (the time it would take one train to go from one side to the other). All the trains on the line in a given direction should then be distributed evenly along this timeline in increments of the "average time between trains" + "waiting time at the station" as you already did.

Assumptions:

  • 1m 30s travel time between stations
  • 1m 00s waiting time per station
  • 3m 00s between trains
  • 21 Stops per line
  • 14 lines

Based on these assumptions we take a total of 2m30s per stop. Now I would also assume that the trains changing direction at the end of the line take the equivalent of one stop to do so, so let's change the average amount of stops per line to 22.

Now the length of our timeline can be calculated as 22stops * 2m30s = 55min.

If there is a train every 3 min we can round the number of trains per leg to 14 (55min/(3min+1min)).

So the total number of trains would now be 14 trains per leg * 2 legs * 14 lines = 392 trains.

Obviously, the assumptions make a major difference, so changing the time between trains to 2min will lead to 504 trains at peak time.

Hope that helps!

Hey,

I am new to this too, but I think I have some ideas for your problem.

Your approach looks good, but I think you have a mistake in how you time the trains. You say that there is one train every three stations and that it takes 1m30s to travel the distance from one station to the next. But how long does the train spend at each station?

My approach would be to represent each line as a timeline (the time it would take one train to go from one side to the other). All the trains on the line in a given direction should then be distributed evenly along this timeline in increments of the "average time between trains" + "waiting time at the station" as you already did.

Assumptions:

  • 1m 30s travel time between stations
  • 1m 00s waiting time per station
  • 3m 00s between trains
  • 21 Stops per line
  • 14 lines

Based on these assumptions we take a total of 2m30s per stop. Now I would also assume that the trains changing direction at the end of the line take the equivalent of one stop to do so, so let's change the average amount of stops per line to 22.

Now the length of our timeline can be calculated as 22stops * 2m30s = 55min.

If there is a train every 3 min we can round the number of trains per leg to 14 (55min/(3min+1min)).

So the total number of trains would now be 14 trains per leg * 2 legs * 14 lines = 392 trains.

Obviously, the assumptions make a major difference, so changing the time between trains to 2min will lead to 504 trains at peak time.

Hope that helps!

12

Related BootCamp article(s)

Brain Teasers

Learn how to tackle brain teasers and what purpose they serve in consulting case interviews

1 Q&A

Related case(s)

Brain Teasers - U2 Concert

Solved 9.5k times
Brain Teasers - U2 Concert Number sequence Situation: “You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then, the other person will say a number that is greater than the first number. The difference between both numbers must be between 1 and 10. We will keep going back and forth in this way until one of us says the number 50. That person wins. You will start.”   Question: What number should you start with? U2 Concert Situation:  U2 has a concert that starts in just 17 minutes. To get there, all the band members must cross a bridge. Since the bridge is old, a maximum of two people can cross the bridge at any one time. To make matters worse, it is dark and there is only one torch. Anyone crossing the bridge must carry a torch. The torch cannot be thrown across the bridge. Instead, someone must walk it back to the other side. Each band member walks at a different speed. If two members cross at the same time, both must walk at the speed of the slower band member. Bono takes 1 minute to cross. Edge takes 2 minutes to cross. Adam takes 5 minutes to cross. Larry takes 10 minutes to cross. Question: Can the band make it to the concert in time? How will they manage this? Buckets Situation: You have a 5-gallon bucket and a 3-gallon bucket. (Assume that you have an unlimited supply of water and that the buckets do not have any markings for measurement. Question: How can you get 4 gallons of water into the 5-gallon bucket? Cigars Situation: A homeless man collects cigar butts. He uses 5 cigar butts to make a new cigar. Today, he has collected 25 cigar butts. Question: How many cigars can he smoke?
4.3 5 402
| Rating: (4.3 / 5.0) |
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Number sequence Situation: “You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then, the other person will say a number that is greater than the first number. The difference between both numbers must be between 1 and 10. We will keep going back and forth ... Open whole case

Brain Teasers - Motel

Solved 8.4k times
Brain Teasers - Motel Motel Situation: Three friends check into a motel for the night. The clerk tells them the bill is $30, payable in advance. They each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day! Question:  Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 that was originally spent. Where did the other dollar go? Murder Situation: The midnight train is coming down the mountains. Art Farnanski seems to be sleeping in his seat. At the station, all the passengers get off the train except one. The conductor comes and taps him on the shoulder to let him know they have arrived. Art Farnanski does not answer. He is dead. Hours later the four people that had shared the train compartment with the dead man are at the police station. The man in the dark suit: "I'm innocent. The blonde woman was talking to Farnanski." The blonde woman: "I'm innocent. I did not speak to Farnanski." The man in the light suit: "I'm innocent. The brunette woman killed him." The brunette woman: "I'm innocent. One of the men killed him." Question: The police detective comes up to you and says: “I know that four statements are wrong and four are true. Who killed Farnanski? (Only one person is guilty).” Trees Statement: You have 10 trees and you have to plant them in five rows, but each row must contain 4 trees. Question: How is this possible?
4.6 5 451
| Rating: (4.6 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Motel Situation: Three friends check into a motel for the night. The clerk tells them the bill is $30, payable in advance. They each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 ... Open whole case

Brain Teasers - Pirates

Solved 7.0k times
Brain Teasers - Pirates Pirates Situation: Five pirates are trying to split up 1000 gold pieces. The rules are as follows: Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote. The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.                        Question: What is the highest amount of gold pieces that pirate #1 can keep and what would his proposal be?             Chicken Situation: A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He arrives at a river and needs to cross it. He finds a small boat that can carry only him and one animal.          Question: How does he get himself, the fox and the two chickens across the river safely?
4.5 5 404
| Rating: (4.5 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Pirates Situation: Five pirates are trying to split up 1000 gold pieces. The rules are as follows: Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose ... Open whole case

Brain Teasers - Firefighter

Solved 6.6k times
Brain Teasers - Firefighter Firefighter Situation: A firefighter stood on the middle rung of a ladder, spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs. After some minutes he was able to climb 18 rungs to the very top of the ladder. Question: How many rungs did the ladder have? Bartender Situation: There are two twin old men that go into the same bar every day. The bartender at the bar hates one of the twins, but there is only one way he could tell the difference between them: The one that he hates drinks very slowly and the one that he likes drinks fast. One day the bartender decides to kill the one that he hates. So when they came in that day he put the same amount of the drink in their cups, the same amount of ice, and the same amount of poison. When they are both done with their drinks the one that the bartender hates dies, but the one he likes lives. Question: How is this? Hats Situation: There are 4 people sitting in a row, trying to win a riddle. The one in front was wearing a red hat. The second from the front was wearing a blue hat. The third from the front was wearing a red hat. The last was wearing a blue hat and is blind-folded. Each of them was informed that they are all wearing a hat, the last person is blind-folded and that there are 2 red and 2 blue hats. They can only see the persons in front of them and are not allowed to turn around and see behind them. Question: The one who guesses the color of his hat wins the prize. Who is it?  
4.5 5 65
| Rating: (4.5 / 5.0) |
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Firefighter Situation: A firefighter stood on the middle rung of a ladder, spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs. After some minutes he was able to climb 18 rungs to the very top of the ladder. Question: How m ... Open whole case

Brain Teasers - Lethal Duel

Solved 5.9k times
Brain Teasers - Lethal Duel Duel Situation: Three men, Adam, Bertie and Charlie, agree to take part in a lethal three-way duel. They each have a pistol and several rounds of ammo, and they draw lots to see who will shoot first and who second. Then they stand an equal distance apart, and they take turns to fire. When it is a player's turn, he can take one shot at any target of his choice. Then, the turn passes to the next player. The duel continues until only one player is left alive. For simplicity, we can ignore the possibility of a player becoming injured and unable to shoot: a player is either alive or dead. We also assume that each player chooses to play in such a way as to give himself the best chance of winning. Now Adam and Bertie are crack shots and will always get a kill, but Charlie is only a moderate shot and will only get a kill two thirds of the time. All three men know this. Question: Of the three men, who has the best chance of winning the duel? Murder Situation: A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. Question: The police instantly arrested the murderer. Who did it and how did they know? Boxes Situation: Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you're told that each of the labels is wrong. You may reach into one of the boxes and pull out only one marble. Question: Which box should you remove a marble from to determine the contents of all three boxes?
4.5 5 85
| Rating: (4.5 / 5.0) |
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Duel Situation: Three men, Adam, Bertie and Charlie, agree to take part in a lethal three-way duel. They each have a pistol and several rounds of ammo, and they draw lots to see who will shoot first and who second. Then they stand an equal distance apart, and they take turns to fire. When it is a ... Open whole case

Similar questions

Estimate the number of videos seen per day on Youtube?
What is the best approach to tackle a guesstimate?
Estimate the number of whatsapp messages sent per day?
Estimate the number of planes that are in the air in an hour?
Estimate the number of houses in the US?
How many miles of road are there in the US?
How would you estimate the cost of Boeing 747?
Market sizing - Q&As
estimate the number of employee of any nationalized bank?
Market sizing question : subway passengers
Ask new question