Math Is Fun Forum

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Horse distance

A horse travels the same distance every day. Oddly, two of its legs travel 30 miles each day and the other two legs travel nearly 31 miles.

How is this possible?

This is just your everyday, common garden-variety, Joe Average kind of adult horse, of medium build and normal conformation.

Bonus questions once you've solved it:-

Last edited by phrontister (2009-08-17 21:49:33)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Horse distance

the horse travels in a curve so the 2 left legs travel shorter than the 2 right legs?

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Horse distance

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Horse distance

Hi phrontister;

If 1a2b3c2212 is right, that curve is not a circle.

---

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.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Horse distance

Hi Bobby,

If 1a2b3c2212 is right, that curve is not a circle.

It isn't necessarily a circle, but it can be. I've reworded the bonus question to remove any doubt about it.

Thanks for alerting me to that.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Horse distance

Hi 1a2b3c2212,

You got it...nice!

I've just got a couple of comments about your answers to the bonus questions:

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Horse distance

was bout to discover the ambiguity of the bonus qn until bobbym said it . it can be any shape right?? just have to switch direction and 0 displacement.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Horse distance

Hi 1a2b3c2212,

was bout to discover the ambiguity of the bonus qn until bobbym said it

After I saw Bobby's post I edited my original post yesterday to try to remove any ambiguity. Maybe there are other loopholes I haven't plugged, but my idea was that the horse goes round and round in circles...like one might do at a mill. And so I introduced my bonus question with "Assuming the horse travels in a circle:".

it can be any shape right?? just have to switch direction and 0 displacement.

The shape in the original (non-bonus) question isn't specified...it just has to be such that results in the 1 mile distance difference within one day.

Last edited by phrontister (2009-08-19 02:34:04)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Horse distance

Hi;

I think that the circle is the best shape for getting the maximum distance between the horses hoofs.

---

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.

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Horse distance

size of the route is not essential right?

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Horse distance

Hi Bobby,

I think that the circle is the best shape for getting the maximum distance between the horses hoofs.

It maintains a consistent increase in the distance difference.

To achieve that 1-mile hoof difference over 30.5 miles (centre of horse's torso), would travelling in a spiral give the same result as for travelling in circles? Too hard for me.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Horse distance

Hi 1a2b3c2212,

size of the route is not essential right?

"two of its legs travel 30 miles each day and the other two legs travel nearly 31 miles".

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Horse distance

but the qn didn't say how big the circle was. could be so big that in 1 day the horse already travel 1 mile leg difference.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Horse distance

but the qn didn't say how big the circle was. could be so big that in 1 day the horse already travel 1 mile leg difference.

Impossible! The horse would have to be 840 feet wide! See my reasoning in post #6 re the single-lap scenario.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Horse distance

oh ya..