How long was he walking?

Every day, Jack arrives at the train station from work at 5 pm. His wife leaves home in her car to meet him there at exactly 5 pm, and drives him home. 

One day, Jack gets to the station an hour early, and starts walking home, until his wife meets him on the road. They get home 30 minutes earlier than usual. How long was he walking? 

Distances are unspecified. Speeds are unspecified, but constant.

Give a number which represents the answer in minutes.

He must be walking for....minutes. Click to know! 

Jack's Walking Duration in Journey!

What was the question?

It's important to think from wife's point of view in the case.

Ideally, had Jack somehow informed earlier his wife about his 1 hour early arrival then his wife's (and his as well) total 60 minutes in round trip would have been saved. 

30 minutes of her round trip are saved which means only 15 minutes of each leg of her trip must have been saved. That is she meets her husband only 15 minutes earlier on the day instead of 60 minutes earlier (if Jack had informed her earlier). 

Hence, Jack must be walking for 45 minutes.

Let's understand this with example.

Suppose wife needs exactly one hour to reach the station every day. She leaves home at 4 PM everyday and reach station at 5 PM & drive Jack home at 6 PM

On one day, Jack arrived at 4 PM and started walking whereas wife leaves home at the same time as usual. They reach home at 5:30 PM.

30 minutes of wife saved indicates that she took 45 minutes to meet husband (instead of 1 hour) at 4:45 PM (instead of 5PM, only 15 minutes earlier) and took him to home at 5:30 PM (instead of 6PM) in next 45 minutes (instead of 1 hour) thereby saving 15 + 15 = 30 minutes only.

Since, Jack started walking at 4 PM and meet her wife at 4:45 PM, he must be walking for 45 minutes.   

The Tunnel Trouble!

A man needs to go through a train tunnel to reach the other side. He starts running through the tunnel in an effort to reach his destination as soon as possible. When he is 1/4th of the way through the tunnel, he hears the train whistle behind him. 

Assuming the tunnel is not big enough for him and the train, he has to get out of the tunnel in order to survive. We know that the following conditions are true - 

1. If he runs back, he will make it out of the tunnel by a whisker.

2. If he continues running forward, he will still make it out through the other end by a whisker.

What is the speed of the train compared to that of the man?

The train must be traveling at THIS speed!

Escape From The Tunnel Trouble!

What was the question?

LOGICAL APPROACH : 

As per condition, if the man runs back he will make it out of the tunnel by a whisker. That means while he runs back 1/4 th tunnel distance, the train travels from it's position to the start of the tunnel. 

In other words, the time taken by man to get back covering 1/4th to the start of the tunnel and the time taken by train to reach at the start of tunnel is same.

So if the man decides to go forward then by time the train reaches at the start of tunnel, man covers another 1/4th tunnel distance i.e. he will be halfway of the tunnel.

At this point of time, the man needs to cover another 1/2th tunnel distance while train has to cover entire tunnel distance. Since, man just manages to escape from accident with train at the exit of tunnel, the train speed has to be double than man's speed as it has to travel distance double of that man travels.

MATHEMATICAL APPROACH : 

Let us suppose - 

M - Speed of Man

T - Speed of Train

D - Tunnel Distance/length

S - Distance between train and the start of tunnel.

As per condition 1, 

Time needed for man to get back at the start of tunnel = Time needed for train to cover distance F to arrive at the start of tunnel

(D/4)/M = S/T  

D/4M =  S/T  .....(1)

As per condition 2,

Time needed for man to move forward at the end of tunnel = Time needed for train to cover distance S + time needed to cover tunnel distance.

(3D/4)/M = S/T + D/T 

Putting S/T = D/4M,

3D/4M - D/4M = D/T

2D/4M = D/T

T/M = 2

T = 2M.

That is speed of the train needs to be double of the speed of the man.

Interestingly, from (1),

D/S = 4M/T

D/S = 2 

D = 2S

S = D/2

That is train is 1/2th tunnel distance away from the start of tunnel. 

A Man Walking on Railroad Bridge

A man is walking across a railroad bridge that goes from point A to point B. He starts at point A, and when he is 3/8 of the way across the bridge, he hears a train approaching. The train's speed is 60 mph (miles per hour). The man can run fast enough so that if he turns and runs back toward point A, he will meet the train at A, and if he runs forward toward point B, the train will overtake him at B.

How fast can the man run?


He must be running at 'this' speed! 

Speed Needed For Run on Bridge

Why to calculate the speed?

If the man turns back and runs towards A for 3/8 of distance while train reaches at the point A. That means the train train reaches at point A when man runs for 3/8 distance.

So if man continues to run towards point B then, while he covers 3/8 distance the train reaches at point A. Now, man is 3/8 + 3/8 = 6/8 = 3/4 distance away from the point A where B is 1/4 away from him now.

Again, we know, the train will overtake the man at point B covering total distance between A and B. Till then man can run only 1/4 th distance between A and B to reach B.That mean the train must be 4 times faster than the speed of man.

Since, train is traveling at 60 mph, the speed of man = (1/4)x60 = 15 mph.

"When is the train?"

Lonnie is taking the train to the Library. He tells Rosti the hour of his train’s departure and he tells Ann at which minute it leaves. He also tells them both that the train leaves between 0600 and 1000.

They consult the timetable and find the following services between those two time:

0632 0643 0650 0717 0746 0819 0832 0917 0919 0950
 
Rosti then says “I don’t know when Lonnie’s train leaves but i am sure that neither does Ann”

Ann Replies “I didn’t know his train, but now I do”

Rosti responds “Now I do as well!”

When is Lonnie’s train and how do you know?

THIS is how you should know the correct time!

Similar Kind of Puzzle! 

Scheduled Time of Lonnie's Train

What was the puzzle?

Lonnie tells Rosti the hour of his train’s departure and he tells Ann at which minute it leaves.

Rosti and Ann consult the timetable and find the following services between those two time: 

0632 0643 0650 0717 0746 0819 0832 0917 0919 0950

Rosti then says “I don’t know when Lonnie’s train leaves but i am sure that neither does Ann”

Ann Replies “I didn’t know his train, but now i do”

Rosti responds “Now I do as well!”

----------------------------------------------------------------------

1. If Ann had 43 as a number representing the minutes then she would have an idea of exact time of Lonnie's train as 0643 straightaway as 43 appears only once in the list.

But she says in her statement that she didn't know his train (initially). Hence, she must not had number 43.

2. Similarly, Ann must not had 46 as well as it appear only once in the list in form of 0746.

3. Now, let's think from Rosti's point of view for a moment. How he was sure that Ann too doesn't know the exact time.

Had he got number 6 (or 7) then what he would have thought - 

"Ann might have got 43 (or 46) and hence may know the exact time as 0643 (or 0646). Or she might not have the exact time if she has got any other number. 

I'm not sure whether Ann knows or doesn't know the exact time"

Since, Rosti is sure that Ann too doesn't know the exact time he must not have got number 6 or 7. 

So all timing with 6 and 7 hours in are eliminated leaving behind timing with 8 and 9 hours as - 

0819 0832 0917 0919 0950

4. Ann is smart enough to list out above timings as possible timings after Rosti's first statement.

Now if Ann had number 19 then she would have been confused with 2 timings 0819 and 0919. 

Since, she is sure that she has got correct time it must be among - 0832 0917 0950 where minutes are appearing uniquely.

5. What if Ann had got 17 (or 50) and she deduced correct time as 0917 (or 0950) ? 

That means Rosti must had number 9. With that number, how he would know the correct time whether it is 0917 or 0950?

Since, in his next statement he say that he too know the correct time he must have got number 8 and that's how he know the correct time is 0832.

And since Ann got number 32 with which she is sure that the correct time is 0832.  

 

Story of Man Having 2 Girlfriends

A man who lives in Middletown has two girlfriends, one in Northtown and one in Southtown. 

Trains from the Middletown train station leave for Northtown once every hour. Separate trains from the station also leave for Southtown once every hour. No trains go to both Northtown and Southtown.

Each day he gets to the Middletown train station at a completely random time and gets onto the first train that is going to either Northtown or Southtown, whichever comes first.

After a few months, he realizes that he spends 80% of his days with his girlfriend from Northtown, and only 20% of his days with his girlfriend from Southtown.

How could this be?

THIS could be the reason behind it! 

Behind Unfair The Number of Visits

What's the story behind the title?

The man arrives at Middletown train station at a completely random time of the day. 

Let's take a look at what happens when he arrives at random time of the day.

After arrival on the station, he is likely to get the train in next hour for sure.

After arriving at random time, there are 80% chances that the first train arriving at the station is heading towards Northtown and 20% chances are there the train is heading towards the Southtown. 

That is there has to be 80% minutes of hour (80% of 60 = 48 minutes) where the first train after is heading towards Northtown and 20% minutes of hour where the next train is heading towards Southtown (20% of 60 = 12 minutes).

So, the trains heading towards the Southtown must be scheduled 12 minutes apart from train heading towards the Northtown.

For example, if trains heading to Northtown are scheduled at 9:00 AM, 10:00 AM, 11:00 AM.......etc then the trains to the Southtown must be scheduled at 9:12 AM, 10:12 AM, 11:12 AM.....etc.

With arrival in 48 minutes past 9:12 AM, 10:12 AM etc, he must be getting the Northtown train and if arrived in 12 minutes past 9:00 AM,10:00 AM etc, he would be getting the Southwest train.

Remember, the timing given are for examples only. The Northwest trains may be scheduled at 9:48 AM, 10:48 AM,......etc and Southwest may be scheduled at 10:00 AM, 11:00 AM.

Key is they leave 12 minutes apart, so that 60 minutes of hour are divided into 48 minutes ahead of Northwest train and 12 minutes ahead of Southwest train. 

A Railway And Cyclist Crossing

A road runs parallel to a railway until it bends to cross it, as shown. A man normally cycles to work along the road at a constant speed of 12 mph, and when he reaches the crossing he’s normally overtaken by a train traveling in the same direction. One day he was 25 minutes late for work and found that the train passed him 6 miles before the crossing. 

What was the speed of the train?

Skip To Know The Speed Of The Train! 

To Cross The Cyclist...

What was the scenario?

 Let's suppose he reaches the crossing at 9:00 AM. Usually at 8:30 AM he is at point A, 6 miles before the usual crossing point B (speed of 12 mph, means 6 mile per half hour).

On the day on which he was late by 25 minutes, he must be again at point A (i.e. 6 miles ahead of usual crossing point B) at 8:55 AM. So at this point, both train and man were at the same point A. And the train as everyday, reaches point B at 9:00 AM. That means, it travels 6 miles in 5 minutes. Hence, train must be traveling at 72 mph.  

Who Is The Engineer?

On a train, Smith, Robinson, and Jones are the fireman, the brakeman, and the engineer (not necessarily respectively). Also aboard the train are three passengers with the same names, Mr. Smith, Mr. Robinson, and Mr. Jones.

(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.

Who is the engineer?

Want to know who? Click Here! 

That's Why Smith Is An Engineer!

Would you like to read question first? 

Let's list all the clues once again here.

(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.

Since as per (2), the brakeman lives exactly halfway between Chicago and Detroit, locations Chicago or Detroit can't be nearest to him. Hence, the passenger that (4) is suggesting must be nearer to brakeman than Chicago and Detroit.

Now as per (1), Mr. Robinson lives in Detroit, means he is not the nearest to brakeman. Mr.Jones earning is $20,000/year as per (3), which is not evenly divisible by 3. Hence, the passenger (4) is pointing is not Mr.Jones.

So neither Mr. Robinson not Mr.Jones but Mr.Smith is the nearest neighbor. 

Now Mr. Robinson lives in Detroit and Mr.Smith is living in between Chicago and Detroit but nearer to brakeman. Hence, Mr. Jones must be living in Chicago.

According to (6), Jones must be name of the brakeman as he is sharing his name with the man living in Chicago.

And if Smith is not fireman as per (5), he must be an engineer!   

  

Motivated Man in Depression

A man in depression decided to commit suicide. He started walking along a railway track when he spotted an express train speeding towards him. Suddenly he changes his mind & decides not to suicide. To avoid it, he jumped off the track, but before he jumped he ran ten feet towards the train. 

Why?

Why did he do so? Click here to know! 

Logical Move By Depressed Man

Why his life was in danger? 

Since the man was firm on his decision of ending his life he started to walk on a railway bridge. By doing that, he made sure no body would save him & even if he falls in river, the death is sure as he didn't know swimming. After crossing the bridge more than half way, he changed his mind. Now by running back wouldn't be feasible option as train was speeding towards him at greater speed. Only way to save life was cross the bridge before train hits him.

Hence he ran 10 feet towards the train & jumped off the track thereby to save his life.

Bird's Journey From Train To Train

Suppose distance between SECUNDERABAD & CST is 1000 KM. Railway tracks are in straight lines with no curves in between.

A train with uniform speed of 100 kmph departs from CST at 9:00 AM. Same day on same track other train from SECUNDERABAD departs at 10:00 AM with uniform speed of 80 kmph.

A bird sitting on engine of train that departed from CST starts traveling toward the SECUNDERABAD & after touching the engine of that train travels back to CST train. A bird repeats this until trains collide.

How much distance the bird traveled & how many times did it travel to & fro? 

Click for the answer! 

Distance Traveled By The Bird

Here is the question! 

Let's divide answer in 2 parts.

1.Finding distance traveled by the bird.

The SECUNDERABAD train is one hour late till then CST train covers 100 km.

Hence effective distance is 900 km

Total speed of approach = 100 + 80 kmph

Total distance covered = 900 km

Time passed before trains collide = 900/180 = 5 Hours

Speed of bird = 120 kmph

Distance covered in 5 hours by bird = 120 * 5 = 600 km

Distance covered in first hour by bird = 120 km

Total distance = 600 + 120 = 720 km



2. Finding how many times bird traveled back & forth.


1st travel -

Total speed of approach = 120 + 80 = 200 kmph

Total distance to be covered = 900 km

Time required to meet each other = 900/200 = 4.5 Hours.
 
2nd travel -

Distance traveled by CST train in 4.5 hours = 100 x 4.5 = 450km

Distance traveled by SECUNDERABAD train in 4.5 hours = 80 x 4.5 = 360 km

Distance between 2 trains = 900 - (450+360) = 90 km

Time left for collision is 5 - 4.5 = 0.5 hrs.


So bird ends up with 1 complete round.