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Each day a man meets his wife at the train station after

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Each day a man meets his wife at the train station after [#permalink] New post 01 May 2010, 08:41
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Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?

A. 45 minutes
B. 50 minutes
C. 40 minutes
D. 55 minutes
E. 35 minutes
[Reveal] Spoiler: OA
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Re: How much time did the man spend walking? [#permalink] New post 01 May 2010, 09:18
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neoreaves wrote:
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?


A� 45 minutes

B� 50 minutes

C� 40 minutes

D� 55 minutes

E� 35 minutes


Is it B ? from the question stem we can see that his wife drove for 20 mins less. Lets plug in numbers to make it simple..

say for e.g every day his wife leaves her house by 4PM, reaches station at 5 PM and reaches back home at 6 PM. Now today they reached at 5:40 PM so that means his wife drove 10 mins less at each side ( 10 mins while going to station and 10 mins while coming back from station). Which means she picked him at 4:50 PM, also from the question stem we know that man's train reached one hour earlier which means 4 PM so that means the man walked for 50 mins...!

I hope I am able to explain..!

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PS : This is a PS question and should have been posted in PS forum.
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Re: How much time did the man spend walking? [#permalink] New post 01 May 2010, 09:20
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neoreaves wrote:
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?

A. 45 minutes
B. 50 minutes
C. 40 minutes
D. 55 minutes
E. 35 minutes


As they arrived 20 minutes earlier than usual, they saved 20 minutes on round trip from home to station (home-station-home) --> 10 minutes in each direction (home-station) --> wife meets husband 10 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-10 minutes=50 minutes.

Answer: B.

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a man arrives at a train station 1 hr earlier [#permalink] New post 26 Aug 2011, 06:25
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Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?


A) 45 minutes
B) 50 minutes
C) 40 minutes
D) 55 minutes
E) 35 minutes

[Reveal] Spoiler: Solution
This isn't so hard if you look at it from another perspective.
We know that the wife left at the time that she normally leaves, because she had no idea that the husband had arrived early. We know that the wife and husband arrived home 20 minutes earlier than usual, even though the wife left home at the regular time. For them to arrive home 20 minutes early, the wife would have had to have encountered the husband after he had walked the distance covered by 10 minutes of travel in a car. 20 minutes would be saved because the wife would save the 10 minutes that would have been required to drive from the point she saw her husband to the station, as well as the ten minutes back from the station to the point she saw her husband.

So, let's say the husband usually arrives at 3pm. Today he arrives at 2pm. The wife leaves 2:30pm to pick him up. She will meet up with the husband at 2::50 pm, because of the above analysis (by meeting up with him at 2:50, rather than her normal 3 o'clock meeting, she saves 10 minutes from husband to station, and back from station to husband, and they arrive home 20 minutes early, as stated in the facts.

So, husband begins walking at 2pm, and wife meets up with him at 2:50=50 minutes. It does not matter which numbers you plug in for the time, the result is always the same. If husband arrives usually at 4:30pm, then that means today he arrived at 3:30 pm. Wife needs to meet up with him at 4:20 pm to save the 20 minutes back and forth. 3:30-4:20=50 minutes.

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Re: a man arrives at a train station 1 hr earlier [#permalink] New post 26 Aug 2011, 10:17
Let t be the time that the man spends walking. Let w be the man's speed of walking. Let v be the car's speed. Let d be the distance from the train station to the couple's home.

Then t + (d-wt)/v = d/v + 1 - (20/60)
[Time taken by man to walk + time taken by the couple to cover the rest of the distance in the car = Time taken by the couple to cover the entire distance from the station to their home in the car + one extra hour as the man had arrived an hour early - 20 minutes earlier that they reach]

Also wt/v + t = 1
[Time taken by man to walk from the station to where his wife picks him up + Time that the wife would have taken to go to the station had the man not walked = 1 hour]

Solving these two equations for t (note that d/v gets eliminated and wt/v gets substituted),
we get 2t = 5/3
=> t = 5/6 hours or (5/6)*60 = 50 minutes

The answer is (B)
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Re: a man arrives at a train station 1 hr earlier [#permalink] New post 29 Aug 2011, 07:01
MBAhereIcome wrote:
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?


A) 45 minutes
B) 50 minutes
C) 40 minutes
D) 55 minutes
E) 35 minutes



This sounds like a puzzle to me. They save 20 mins driving to and fro from the meeting junction to the station, 10 mins each side. So, if the man didn't walk at all, his wife would be there in the station in 10 minutes for sure. Daily his wife picks him @ say 5PM. So, it must be 4:50(10 minutes before 5:00) when they met. The man started walking @4:00(1 hour early). He must have walked 50 minutes when they met.

Ans: "B"
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Re: a man arrives at a train station 1 hr earlier [#permalink] New post 29 Aug 2011, 13:11
I was not able to solve this problem, also the methods mention above didnot help, can any one explain me.
I was able to solve this problem only to the extent at

Every day
By Car:
Arrival at station : 5:00 PM
couple reach home: 5:30 PM
So time taken 30 mins

today
Car + walk
Arrival station at: 4:00 PM
Reach home: 5:10 PM
Time taken 70 mins

then how do i go ahead calculating it?
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Re: a man arrives at a train station 1 hr earlier [#permalink] New post 04 Sep 2011, 05:46
kuttingchai wrote:
I was not able to solve this problem, also the methods mention above didnot help, can any one explain me.
I was able to solve this problem only to the extent at

Every day
By Car:
Arrival at station : 5:00 PM
couple reach home: 5:30 PM
So time taken 30 mins

today
Car + walk
Arrival station at: 4:00 PM
Reach home: 5:10 PM
Time taken 70 mins

then how do i go ahead calculating it?


the question is "How much time did the man spend walking?"

it is a 30mins drive, so wife leaves home at 4:30 PM. we know that the couples reached 20mins early, so the wife drove 10mins less each direction. that means when she saw her husband when she had driven for 20mins (10 mins less than the usual 30mins). so, the wife saw her husband at 4:50 PM.

at this point, the husband had been walking for 50 mins, because he started walking at 4:00 PM.
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Re: a man arrives at a train station 1 hr earlier [#permalink] New post 04 Sep 2011, 21:25
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kuttingchai wrote:
I was not able to solve this problem, also the methods mention above didnot help, can any one explain me.
I was able to solve this problem only to the extent at

Every day
By Car:
Arrival at station : 5:00 PM
couple reach home: 5:30 PM
So time taken 30 mins

today
Car + walk
Arrival station at: 4:00 PM
Reach home: 5:10 PM
Time taken 70 mins

then how do i go ahead calculating it?


The explanation given by fluke is spot on. You don't really need to calculate anything here. If you do try that way, you will have to take tons of variables and make tons of equations... Try reasoning it out.
They arrived 20 minutes early. Why? Because his wife drove less. Why? Because she met him on the way. Why do they usually take 20 mins more? Because she takes another 10 minutes to reach the station and then 10 more minutes to drive back that same distance.
Say the train reaches at 12, the wife usually reaches the station at 12 and is 10 minutes away from the station at 11:50. This is the point where she met him today since she had to travel 10 minute distance less. Why? Because he got down at the station at 11 today and started walking. How long did he walk? At 11:50, he reached the point where his wife is 10 minutes away from the station. So he walked a total of 50 minutes.
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Re: Each day a man meets his wife at the train station after [#permalink] New post 03 Aug 2013, 12:55
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?

Lets say normally he get's in at 6 and they get home at 7. Today, he get's in at 5 and they get in at 6:40. However, because the man starts walking and moves closer to his home when his wife picks him up, the amount of time he spends in the car with her will not be an hour as usual, but less. He travels (walk+car) for a total of 100 minutes. If they arrive 20 minutes earlier than usual, that means the distance (and time) his wife covered is less because his walking reduced the distance between himself and home. His wife normally drives an hour. (as established, she picks him up at 6 and arrives at 7)...From here on, I am lost. How does the fact that they arrived 20 minutes earlier tell us that he walked for 50 minutes? If the question said that the round trip took 20 minutes less than normal then I could understand how each leg of the trip was reduced by 10 minutes, but the question says that it took them 20 minutes less time to get home from normal when the husband got picked up at his closer-to-home distance.

This problem is without question one of the hardest and most frustrating I have encountered. I don't understand why we care about the round trip of the wife. If it normally takes him and her one hour to get home and today they arrived 20 minutes earlier doesn't that apply just to the leg of the trip? I could see this, perhaps, if her trip was reduced by 20 minutes (i.e. the round trip) but its only the second half which the two of them both travel that is reduced by 20 minutes. This means that the round trip would be reduced by 40 minutes but again, how does this help us?

Heeeeeeeeelp!















A. 45 minutes
B. 50 minutes
C. 40 minutes
D. 55 minutes
E. 35 minutes
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Re: Each day a man meets his wife at the train station after [#permalink] New post 03 Aug 2013, 17:14
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WholeLottaLove wrote:
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?

Lets say normally he get's in at 6 and they get home at 7. Today, he get's in at 5 and they get in at 6:40. However, because the man starts walking and moves closer to his home when his wife picks him up, the amount of time he spends in the car with her will not be an hour as usual, but less. He travels (walk+car) for a total of 100 minutes. If they arrive 20 minutes earlier than usual, that means the distance (and time) his wife covered is less because his walking reduced the distance between himself and home. His wife normally drives an hour. (as established, she picks him up at 6 and arrives at 7)...From here on, I am lost. How does the fact that they arrived 20 minutes earlier tell us that he walked for 50 minutes? If the question said that the round trip took 20 minutes less than normal then I could understand how each leg of the trip was reduced by 10 minutes, but the question says that it took them 20 minutes less time to get home from normal when the husband got picked up at his closer-to-home distance.

This problem is without question one of the hardest and most frustrating I have encountered. I don't understand why we care about the round trip of the wife. If it normally takes him and her one hour to get home and today they arrived 20 minutes earlier doesn't that apply just to the leg of the trip? I could see this, perhaps, if her trip was reduced by 20 minutes (i.e. the round trip) but its only the second half which the two of them both travel that is reduced by 20 minutes. This means that the round trip would be reduced by 40 minutes but again, how does this help us?

Heeeeeeeeelp!


1. Let the wife drive for y minutes till the husband starts from the station.
2. Once the husband starts the let the wife drive for x minutes till she meets him. Thus the husband also walks for x minutes.
3. After meeting her husband the wife drives back for the same duration of x+y minutes
4. The wife totally traveled for 2x + 2y minutes.
5. We actually know that they arrived 20 minutes earlier.
6. If y=0. meaning that the wife had started at the same time as the husband i.e, say at 5 then it means she normally comes at 6 and hence takes 1 hr to travel to the station and totally 2 hrs to and fro. but that day she traveled 20 min less so the duration of the travel is 100 minutes
7. Equating (4) and (6), 2x+2y=100 or x=50 since y=0, we have x is 50 minutes or the man walked for 50 minutes

Note: whatever value we plug in for y, we will get x as only 50 because the difference between the RHS and 2y is always 100. y can also be negative i.e., the wife starts after the husband starts.
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Last edited by SravnaTestPrep on 04 Aug 2013, 02:27, edited 4 times in total.
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Re: Each day a man meets his wife at the train station after [#permalink] New post 04 Aug 2013, 01:28
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Please note that I have edited my reply as I had misread the problem earlier. I apologize for that.
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Re: Each day a man meets his wife at the train station after [#permalink] New post 04 Aug 2013, 11:09
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Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?

Thanks for the reply!

Tell me, does the following line of thinking make sense?

Let's say normally the man get's in at 6 and is home by 7. The wife takes one hour to get from home to the station meaning the round trip is 120 minutes. Today, he get's in at 5 and is home by 6:40. The wife, unaware of her husband getting in earlier, still leaves at 5 PM (so she gets to the station by 6) but today is home by 6:40 meaning she spent a total of 100 minutes on the road both ways, not 120 minutes. If she is making a round trip, this means she would turn around at a point that is 10 minutes closer to home than normal meaning she drove a total of 50 minutes from home to where her husband was and another 50 minutes from where her husband was to home. If she leaves at her normal time of 5PM and she drives a total of 100 minutes to and from the station she would have traveled 50 minutes before she met him which would be at 5:50PM That means he would have walked 50 minutes (from 5:00 to 5:50 then spent another 50 minutes in the car with his wife (from 5:50 to 6:40) before he got home.

I feel physically and mentally drained after this problem! :-D
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Re: Each day a man meets his wife at the train station after [#permalink] New post 04 Aug 2013, 18:03
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WholeLottaLove wrote:
Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?

Thanks for the reply!

Tell me, does the following line of thinking make sense?

Let's say normally the man get's in at 6 and is home by 7. The wife takes one hour to get from home to the station meaning the round trip is 120 minutes. Today, he get's in at 5 and is home by 6:40. The wife, unaware of her husband getting in earlier, still leaves at 5 PM (so she gets to the station by 6) but today is home by 6:40 meaning she spent a total of 100 minutes on the road both ways, not 120 minutes. If she is making a round trip, this means she would turn around at a point that is 10 minutes closer to home than normal meaning she drove a total of 50 minutes from home to where her husband was and another 50 minutes from where her husband was to home. If she leaves at her normal time of 5PM and she drives a total of 100 minutes to and from the station she would have traveled 50 minutes before she met him which would be at 5:50PM That means he would have walked 50 minutes (from 5:00 to 5:50 then spent another 50 minutes in the car with his wife (from 5:50 to 6:40) before he got home.

I feel physically and mentally drained after this problem! :-D


Yes, exactly.

I think this is a very difficult problem and I am sure will not be asked in the actual exam.
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Re: a man arrives at a train station 1 hr earlier [#permalink] New post 21 Aug 2014, 14:21
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Re: a man arrives at a train station 1 hr earlier   [#permalink] 21 Aug 2014, 14:21
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