1. ## find the distance

Starting 3 miles away , a boy walks home at 3 mph.His dog ,starting with him runs home at 5mph, then inmediately turns around, runs back to the boy, then back to the house, back to the boy, and so on until the boy reaches home.How far does the dog run?

2. This is a really good question, you have to be intelligent to see the trick. The point is that it takes the boy 1 hour to walk home because he is walking at a rate of 3mph for 3 miles.

If the dog is running at his rate of 5mph for the same amount of time as the boy is running . . . can you see where I'm going with this?

3. ## von Neumann and the "Fly and Train" Problem

Since this is a reformulation of the Fly and Train problem it might be
worth retelling the anecdote about Jonny Von Neumann's encounter
with it.

I quote form:
http://ei.cs.vt.edu/~history/VonNeumann.html

"One last anecdote about von Neumann's brilliant mathematical capabilities.
The von Neumann household in Princeton was open to many social activities
and on one such occasion someone posed the "fly and the train" problem [4]
to von Neumann. Quickly von Neumann came up with the answer.
Suspecting that he had seen through the problem to discover a simple
solution, he was asked how he solved the problem. "Simple", he
responded, "I summed the series!" [From Nick Metropolis]"

[4] Suppose two trains on the same track are 20 miles apart, heading
towards each other, each traveling at 20 miles per hour. Suppose a fly,
capable of flying at 60 miles per hour leaves the first train, flies to the other,
turns around and flies back and forth until the two trains collide. How far will
the fly travel before it is squashed between the crashing trains?

RonL

4. "I summed the series"

I love it

5. Originally Posted by MathGuru
"I summed the series"

I love it
I'm not sure that we should believe him, I suspect he had his tongue
firmly placed in his cheek ("tongue in cheek" colloquial expressions (in the
UK at least) meaning he may not have been serious )

RonL

6. I saw a similar variation to this problem. Very nice.

7. I've never actually seen the series solution to this problem. Although I'm certain there is one. Anyone care to elaborate?

8. Originally Posted by Treadstone 71
I've never actually seen the series solution to this problem. Although I'm certain there is one. Anyone care to elaborate?
Summing the series is the "bad" way of doing the problem. That if what the problem is in tricking you. There is no need for an infinite series in this problem. Its solution is rather elementary.

9. It doesn't matter. What is the series solution?

10. This is indeed a nice little puzzle!
It's been mentioned before, but most people tend to attack it the wrong way at first. But if you give it a bit of thought, it's not terribly hard