how much time did the train need?

the train took 36 seconds to pass his wife

Originally posted by luskin
the train took 36 seconds to pass his wife

That answer can't be right.

Originally posted by luskin
the train took 36 seconds to pass his wife

Sorry! That is incorrect.

What we can determine is the train must take less time to pass his wife than it does him.

If all velocities are the same he would never catch his wife if the train took the same amount of time or more.

This would mean his wife was going as fast or faster then he was going.

Hey everyone,

I'm sorry, I really forgot about this one cause im having some busy weeks.
So I'll give you an extra detailed solution now because you had to wait so long 🙂

I uploaded a graphic solution which will make the mathmatical solution probably more easy to understand.

http://www.crazyweird.de/trainproblem.jpg

Somehow we have to determine distances. Since we dont know the train lenghts in meters we just calculate with train lenghts as a unit. That way we have eleminated one variable

Note that the graph is from the man's point of view - the man is set as stationary (therefore the train goes into the opposite direction as the woman). This has the advantage that later we have to calculate with 2 velocities only (the train's and the woman's). So another variable was eleminated here. If you want to try it again now, you might be able to solve it. Otherwise just read on.


The red line shows, that the train's beginning is at t=0 (when he reaches the man). After 36 seconds you can see the red line has reached 1 at the x-(vertical)-axis, meaning it is one train-length away. Logically the train end is at 0 now. The train-end line is of course parallel to the train beginning because they are moving with the same velocity 😛

Now comes the tricky part: The woman's movement is in opposite direction as the train, therefore goes from a positive value down to zero train lenghts. In other words: From the man's point of view, the woman is moving towards him (while the train moves away from him).

We know that after 54 seconds she is 1,5 train lenghts away. Now we have to draw a straight line (she has constant velocity) from there to zero train lengths, with the requirement that from the point where her "line" and that of the train's end meet, it's 240 seconds on the horizontal axis. 🙄

Now to the mathmatical solution:

We have 3 unknown variables:
- velocity of train v(t)
- velocity of woman v(w)
- time the train needs to pass the woman (t - this is what we are actually looking for 😉 )

What we know is:

v(t) * 36s = 1 (trainlenghts)
[ v(t) - v(w) ] * t = 1
v(w) * [t + 240s] = -1,5 (graphic solution is helpful here to understand why its -1,5)

So there we go, this can be solved 🙂

Answer is: 30 seconds.

If you can't get to that result with the 3 terms above just tell me 🙂


PS: I just noticed that wherever I wrote 1,5 I meant 1.5 (Germans are just different in everything 😛)

We got that.

If they are riding along a railroad track then they have to get off the track (and presumably are stationary) while the train passes. So it takes the same amount of time to pass each of them.
As`for the answer of 30 seconds, I can't follow that reasoning. I think it takes more than 29.38 seconds and less than 36. Don't know how you get more definite than that.

Originally posted by luskin
If they are riding along a railroad track then they have to get off the track (and presumably are stationary) while the train passes. So it takes the same amount of time to pass each of them.
As`for the answer of 30 seconds, I can't follow that reasoning. I think it takes more than 29.38 seconds and less than 36. Don't know how you get more definite than that.

I do give you points for an attempt at a common logic solution, the question clearly indicates that his wife was to ride ahead.

Please read the question:

when he fixed his bike he starts driving again. after a short time there comes a train, that needs 36 seconds to pass him completely.

Clearly states that they were not, as you presummed, stationary. As the train passes after he begins to pedal again. And his wife said it took 4 minutes for him to catch up with her. So clearly they were not together. bringing us back to my original statement the train must have taken less time to pass his wife.

52 secs if you add the 18 to the 36

Originally posted by luskin
If they are riding along a railroad track then they have to get off the track (and presumably are stationary) while the train passes. So it takes the same amount of time to pass each of them.

They are not actually riding on the track, but next to the track. The stipulation specifically stated that wife, man, and train all had constant speed, which rules out stopping to let the train pass.

Originally posted by Balla88
We got that.

Actually, nobody got it. PBE6 got the correct number, but then claimed there was no solution! You claimed 29.75s, which is 0.25s too few.

Congrats to crazyblue on stumping the lot of us. This problem reminds me why I need a refresher on physics...

Originally posted by BigDoggProblem
Actually, nobody got it. PBE6 got the correct number, but then claimed there was no solution! You claimed 29.75s, which is 0.25s too few.

Congrats to crazyblue on stumping the lot of us. This problem reminds me why I need a refresher on physics...

Yeah, don't remind me. I tried a graphical solution too, thinking I was all hot to trot, but the designation of the train length as 1 and the moving frame of reference are the keys. I have to admit, it was quite a clever solution.

Originally posted by BigDoggProblem
Actually, nobody got it. PBE6 got the correct number, but then claimed there was no solution! You claimed 29.75s, which is 0.25s too few.

Congrats to crazyblue on stumping the lot of us. This problem reminds me why I need a refresher on physics...

I did it in about 1 minute. It was an estimate. Both PBE6 and I got the right answer.

Originally posted by Sci Fi West
52 secs if you add the 18 to the 36

Not quite Sci Fi.

That would be the answer to how long the train took to reach his wife from where he was.

Originally posted by Balla88
I did it in about 1 minute. It was an estimate. Both PBE6 and I got the right answer.

Estimates aren't the same as right answers. All you can correctly claim is that your guess was pretty close to the solution.

90 Seconds