Math Is Fun Forum

anandbrar

Member

Registered: 2011-07-20

Posts: 70

Question about the Girl, Boy n Dog puzzle.

I was just thinking about what should be the answer as to where the dog is now.

Quoting from mathsisfun site:
"A girl, a boy, and a dog start walking down a road.

They start at the same time, from the same point, in the same direction.

The boy walks at 5 km/h, the girl at 6 km/h.

The dog runs from boy to girl and back again with a constant speed of 10 km/h. The dog does not slow down on the turn.

How far does the dog travel in 1 hour?

Solution.
10km. Because the dog's speed is 10 km/h.

Where the boy and girl are has no effect on answering this puzzle.

But if you asked WHERE the dog is after 1 hour … that would be a very hard question to answer."

Could it be done by taking the oscillatory motion of the dog, with constant speed and increasing time period and integrating it?...Or can it be possible that the dog is either close to the boy or the girl?

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"widen your gaze... extend beyond the obvious..."

TMorgan

Member

Registered: 2011-04-13

Posts: 25

Re: Question about the Girl, Boy n Dog puzzle.

Anandbrar,
  I don't know that it would be possible to predict where the dog would be. Think of when the three just start to walk. About a microsecond later the humans are a miniscule distance apart and the dog is bouncing  back and forth a million times a second or so. We are talking infinitesimals here.

It is not hard to visualize the opposite of the process. Imagine a very bouncy ball. You throw it straight down hard and it starts bouncing up and down between two boards. Now the top board starts moving down toward the bottom board. The closer the boards get the faster the ball changes direction. Its frequency increases. Theoretically that frequency will reach infinity just before the boards come together and squash the  oscillation. That is not hard to imagine. But your puzzle is the same thing in reverse. The boards are the people, the dog is the ball. We are asked to decide at what point the distance between the people goes from zero to, say, one over almost infinity. Does the dog go forward or backward first? What is the smallest distance that is not zero? In the real world the first measurable distance is when the signal is first able to be separated from the noise.

Sorry if it seems that I am being abastract and not specific, but my point is that I don't think you can be specific and predict this situation.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question about the Girl, Boy n Dog puzzle.

Hi all;

By making one or two small concessions the problem will have a definite answer while retaining the flavor.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anandbrar

Member

Registered: 2011-07-20

Posts: 70

Re: Question about the Girl, Boy n Dog puzzle.

hi TMorgan,

Yes I get your point..

hi bobbym,

what kind of concessions?...like if we start measuring after 1 second has passed and assume that the dog is with the boy at this instant?

Thanks..

Last edited by anandbrar (2011-08-25 19:05:36)

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"widen your gaze... extend beyond the obvious..."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question about the Girl, Boy n Dog puzzle.

Hi anandbrar;

I believe to solve the problem we only have to insert the conditions that the boy and the girl go first and that the dog chases the girl first. After that everything remains the same. Then I have a discrete solution.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anandbrar

Member

Registered: 2011-07-20

Posts: 70

Re: Question about the Girl, Boy n Dog puzzle.

Hi bobbym,

But if they all start at the same time, then there is no solution possible?

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"widen your gaze... extend beyond the obvious..."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question about the Girl, Boy n Dog puzzle.

Hi;

I think that muddles the question. My solution I think deals with that. It just needs the first target of the dog, boy or girl? After that you can iterate the solution with a very, very tiny lead of the boy and the girl.

In a continuous solution we can think of the boy, girl and dog of being an infinitessimally small distance away ( who started first ). If the lead is infinitessimally small then it is as if they all start at the same time.

For a discrete solution Δt must have some value, no matter how small, it means someone started first.

That is the difference ( no pun intended ) here between a difference equation and a differential equation.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.