BrainDen.com - Brain Teasers
• 0

# A man and his dog

## Question

A man and his dog live at the bottom of a hill. It is their habit every morning to walk the three miles to the top of the hill and then back. Well, time has gone on and the dog has gotten older. The man still walks to the top of the hill every morning, but the dog has gotten older and can't quite keep up with him.

What they now do is this: The man starts out at his usual steady pace and his dog follows but at half his owner's speed. So when the man reaches the top he turns around and starts back down, maintaining the same steady pace. Before long he meets the dog coming up the hill and at this point the dog turns around and starts back down again.

Because they're going down the hill, now the man and the dog walk at the same speed down the hill because the dog doesn't have a hard time keeping up going downhill.

How far does his dog walk?

## Recommended Posts

• 0

4 miles

##### Share on other sites
• 0
A man and his dog live at the bottom of a hill. It is their habit every morning to walk the three miles to the top of the hill and then back. Well, time has gone on and the dog has gotten older. The man still walks to the top of the hill every morning, but the dog has gotten older and can't quite keep up with him.

What they now do is this: The man starts out at his usual steady pace and his dog follows but at half his owner's speed. So when the man reaches the top he turns around and starts back down, maintaining the same steady pace. Before long he meets the dog coming up the hill and at this point the dog turns around and starts back down again.

Because they're going down the hill, now the man and the dog walk at the same speed down the hill because the dog doesn't have a hard time keeping up going downhill.

How far does his dog walk?

okay the dog goes half as fast... so when the man is at the summit, the dog has gone halfway (1.5 miles). Now they are 1.5 miles apart, with the man going at X speed, the dog is going at X/2. So the man will have gone 2/3 the remaining distance (1 mile out of 1.5) and the dog will have gone 1/3 the distance between them (.5 out of 1.5)

When they meet, the dog has gone 2 miles uphill, the man has gone 3 uphill and 1 downhill. But then the dog has to go 2 miles back down with the owner.

The dog has gone 4 miles, the owner has gone 6 miles.

##### Share on other sites
• 0
A man and his dog live at the bottom of a hill. It is their habit every morning to walk the three miles to the top of the hill and then back. Well, time has gone on and the dog has gotten older. The man still walks to the top of the hill every morning, but the dog has gotten older and can't quite keep up with him.

What they now do is this: The man starts out at his usual steady pace and his dog follows but at half his owner's speed. So when the man reaches the top he turns around and starts back down, maintaining the same steady pace. Before long he meets the dog coming up the hill and at this point the dog turns around and starts back down again.

Because they're going down the hill, now the man and the dog walk at the same speed down the hill because the dog doesn't have a hard time keeping up going downhill.

How far does his dog walk?

The dog walks half as fast as the owner - therefore when the owner is at the top the dog is half way up or 1.5 miles. Now ther is 1.5 miles between them. When the owner walks 1 mile he will meet the dog who has walked a half mile. Therefore they met at the 2 mile mark. It is 2 miles home for the dog for a total of 4 miles.

##### Share on other sites
• 0
The dog walks half as fast as the owner - therefore when the owner is at the top the dog is half way up or 1.5 miles. Now ther is 1.5 miles between them. When the owner walks 1 mile he will meet the dog who has walked a half mile. Therefore they met at the 2 mile mark. It is 2 miles home for the dog for a total of 4 miles.

This is the way I figure it.

The incline is 3 miles.

Owner walks up 3 miles

Dog walks up 1.5 miles (half pace of owner)

Owner begins the decline while dog is still going up...so dog is still going half pace of owner and would meet owner half-way between the 1.5 mile mark and the 3 mile mark which would be the 2.25 mile mark.

So if it took the dog to 2.25 miles to meet up with his owner and they go the same pace down after that, the answer would be 2.25 miles up and 2.25 miles down to equal 4.5 miles that the dog traveled compared with the owner's 6 mile trek.

##### Share on other sites
• 0
This is the way I figure it.

The incline is 3 miles.

Owner walks up 3 miles

Dog walks up 1.5 miles (half pace of owner)

Owner begins the decline while dog is still going up...so dog is still going half pace of owner and would meet owner half-way between the 1.5 mile mark and the 3 mile mark which would be the 2.25 mile mark.

So if it took the dog to 2.25 miles to meet up with his owner and they go the same pace down after that, the answer would be 2.25 miles up and 2.25 miles down to equal 4.5 miles that the dog traveled compared with the owner's 6 mile trek.

There's one thing wrong with that: the dog is going half the speed of the owner on its way up even when the owner is coming down. So, when the owner starts descending from 3 miles and the dog is still continuing upward starting at 1.5 miles, they will not meet in the exact halfway mark (that would happen if they were traveling the same speed). Rather, because the man is traveling twice as fast, the man travels 2/3 of the gap back to the dog at the same time the dog travels 1/3 of the gap back up, meeting at 2 miles. Then, after traveling back down another 2 miles, the dog has traveled 4 miles.

##### Share on other sites
• 0
There's one thing wrong with that: the dog is going half the speed of the owner on its way up even when the owner is coming down. So, when the owner starts descending from 3 miles and the dog is still continuing upward starting at 1.5 miles, they will not meet in the exact halfway mark (that would happen if they were traveling the same speed). Rather, because the man is traveling twice as fast, the man travels 2/3 of the gap back to the dog at the same time the dog travels 1/3 of the gap back up, meeting at 2 miles. Then, after traveling back down another 2 miles, the dog has traveled 4 miles.

When the man is at the top of the hill, he has traveled 3 miles. The dog however has traveled half that, (1.5 miles). The man then heads back down the hill, however the dog is still heading up the hill. When they meet, it is half of the remaining 1.5 miles (.75) The dog and the man both now head down the hill. 1.5 the first leg plus the .75 the second leg.

so...

1.50 miles up - 1st leg

.75 miles up - 2nd leg

.75 miles down - 3rd leg

1.50 miles down - 4th leg.

--------------------------------

4.50 - miles

3(m)x2

<-------------------> 3 + .75 + 2.25 = 6 miles the man walked

1.5(d)x2 .75(d)x2

<--------><--> 1.5(2) + .75(2) = 4.5 miles the dog walked

##### Share on other sites
• 0

Its actually 4 miles. I will explain how.

The owner walks 3 miles uphill. The dog walks 1.5 miles. I think everyone agrees upto this point. Now when the owner turns back the dog is still doing half the speed of the owner. Now when the owner has walked one mile down the dog has done only half of that which is 0.5 miles. and that is where they meet. Since now the dog has gone 2 miles up and the owner has walked one mile down(Out of the 3 miles). Now they both walk at the same speed downhill which is 2 miles. So while the owner walks 6 miles in all the dog has walked 4 miles.

Owner- 3 + 1 = 4 + 2 = 6 Miles

Dog - 1.5 +0.5= 2 + 2 = 4 Miles

##### Share on other sites
• 0

Excuse me Ladies and Gentlemen (and sorry for my poor english): Why do you think the dog have the time to go at 1.5 miles in the time the man go at 3 miles? this is the joke

the man go at 3+1,5 miles in the time the dog go at 1,5 miles. they come back togheter and THE DOG WALK FOR 3 MILES. it's right?

##### Share on other sites
• 0
Excuse me Ladies and Gentlemen (and sorry for my poor english): Why do you think the dog have the time to go at 1.5 miles in the time the man go at 3 miles?

Welcome to the boards, BluVermiglio. While walking uphill, the dog walks at half the man's speed. Since it is three miles to the top of the hill, when the man reaches the top, the dog will be at the 1.5 mile mark.

##### Share on other sites
• 0

Yes i answered too fast and it was a mistake.

now understand,

when the man is on top the dog is at 1,5 miles mark so the dog go up 0,5 miles more and the man go down 1 miles in that times

so they meet togheter at 2 miles mark and the dog walked 4 miles total THANKS

Edited by BluVermiglio
##### Share on other sites
• 0

the dogs walked 4 miles altogether

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.