# The Long Walk Home Puzzler is WRONG

This Puzzler came to me from Cartalk by email. It involves a husband who arrives at the train station an hour early, and decides to walk towards home. The train is ontime. The walk cuts down the distance the wife must drive, so they get home 20 minutes earlier than usual. The question is, how long did the husband walk, and no further data was given. The answer given on the next email is wishy-washy logically, and in fact is wrong. I worked a long time on this, and I found the easiest solution by setting up a time line for the husband and the train and the wife. To save you some grief, the problem is under-specified, so that there is no single answer. Something on the timeline needs to be assumed.

The husband walked for 20 minutes. At 49 MPH.

Too many variables. Assume the car goes 30mph, 20 minutes at that speed would be 10 miles. If he walks 10 mph and gets picked up 10 miles from the station, my guess.

If the wife is saed 20 minutes of driving, the husband must walk a lot longer because he walks so much more slowly.

You have over-specified the problem, but a good start. In the spirit of the problem, I think you should add as little new data as possible. When I solved it, I did what the writers did, and added that the train takes one hour between stations. Then I solved for his walking time.

If I was the one walking and my wife the one driving/picking me up, I still couldnâ€™t figure this outâ€¦
These things make my head hurtâ€¦ lol

I worked about 4 hours trying to solve the unsolvable problems. Finally, I found a way to show it was unsolvable.

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Suggest to post two answers that you believe both match the conditions.

My big point is that there are zero answers that match the conditions. If you add to the conditions that the trainâ€™s travel time is given, you can calculate a walking time. However, the people who wrote the answer seem to have forgotten to add on the first hour of walking (assuming they had chosen a one-hour travel time for the train.) They got 50 minutes when I got 60 more. The train has not even arrived at Station #1 at the 50 minute mark!

Does the wording match the wording shown on this websiteâ€™s puzzler page? Scroll to the bottom of this page and click â€śradio showâ€ť.

This website has both the original question and the incorrect answer.

I recommend getting a good mental picture of the movements of the couple. Where do they start, where do they meet, where do they go then.

While I canâ€™t explain how the given explanation is correct, I think 50 minutes is correct. Since they imply it doesnâ€™t matter how far apart the station and the home are and how fast the car and the walker are, I just picked numbers, and for two different cases I got the guy walking for 50 minutes. Try it.

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Think about what the wife would do. One of the limits stated in the problem is that no phone call is made to the wife. If the train trip is long, and they live near the final station, then the wife would NOT leave to pick him up BEFORE the train has left the FIRST station. At t = 50 minutes, the train has not even arrived at the first station. So, the wife is still sitting at home watching TV at the time he has walked for 50 minutes. Hubby will have walked for 60 minutes at the time the train leaves the first station. So, the question is, how long did you assume the train would travel to the second station?

The wife must have saved 20 minutes of her drive-time, 10 minutes each way. So the husband must have saved the same 10 minutes on the way home b/c he rode with her. If he didnâ€™t walk, and just waited for the wife to arrive at the train stations , heâ€™d have arrived home at the same time he usually did; i.e. no time savings if he didnâ€™t walk. Does any of that help?

I believe that you have assumed that the trainâ€™s travel time is 60 minutes. But, hubby started walking an hour before the normal time, so even after your assumption of 60 minutes, the correct answer would be 60 + 50 = 110 minutes.

Now, what if the trainâ€™s travel time is 50 minutes. Then your answer is NOT 50 minutes of walking (or 110) . So, the Puzzler looking for a single answer is incorrect.

I have read and reread the original question, and the â€śno phone call to wifeâ€ť and the lack of a normal travel time for the train seem to make it unsolvable as written.

Doesnâ€™t matter what the travel time of the train is. He rode the train from station 1 to station 2
Wife normally picks him up at station 2, he walked from station 2

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The assumption is that the trainâ€™s travel time is the same from station to station; i.e. it doesnâ€™t change with the earlier departure time. In other words the husband arrived at the destination station exactly one hour earlier than he usually did, b/c he departed one hour earlier. That might be an invalid assumption, traffic is different etc, but that assumption is necessary to solve the puzzle.

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Look at this timeline comparing the Normal trip to the Walking trip. ANSWER: 120 minute walking time.

Since the answer to this Puzzler is purported to be a single value, it must be independent of many variables. It might be easiest to understand by just putting in reasonable numbers for the timeline that satisfies the conditions of the puzzle. If there is a single answer, it will pop out.**

Spoiler Alert: you will find that this puzzle does not have a single answer. The choice of the travel time for the train will correct that.

TYPICAL EXAMPLE FOR CALCULATING A WALKING TIME:

70 MINUTE TRAIN

We are comparing the Normal Schedule to Todayâ€™s Walking Schedule.

NORMAL TRIP: Two assumptions: The train travels between stations for 70 minutes. The wife has a 20 minute normal trip from the home to the Station #2.)

6:00 Station #1: Hubby arrives and Train departs on time with an ETA of 7:10

6:50 Wife starts towards Station #2, assuming 20 minutes needed to arrive at the Station #2 at 7:10.

7:10 Train arrives, husband picked up and they head 20 minutes to home.

7:30 They arrive home.

Todayâ€™s trip:

5:00 Husband arrives at Station #1 and heads out towards Station #2 on foot.

6:00 Train departs on time with an ETA of 7:10. (Husband has walked for 60 minutes.)

6:50 Wife starts her normal 20 minute trip as usual. (Husband has walked 110 minutes by now.)

7:00 The wife overtakes her husband 10 minutes before the trainâ€™s arrival at Station #2. (120 minutes walking time total.) and they head for home in 10 minutes. The trip has saved 20 min.

7:10 They arrive home 20 minutes early.

Seems youâ€™ve added a complication. Only thing changing is his arrival time at the station. For the one hour earlier arrival time case he starts walking, and they end up home 20 minutes earlier than normal. With those being the only constraints, my calculations show 50 minutes, for any reasonable combination of car speed, walking speed, and distance from the house to the terminal.

Hey, I am getting to the bottom of this, at least for some of you. Some responses to me are based upon Reading #2.

Reading #1: He starts walking when he arrives at Station #1. This is an hour before the train arrives.
Reading #2: He waits at Station #1, and takes the train to Station #2. He then walks and shortens the wifeâ€™s trip. The whole bit about leaving an hour early is pointless. And, his wife is late (again!) picking him up at the Station #2. This actual increase the total time, because the trai n is on time and the wife is late.