You and Your Dog: A Mile Run Up and Down the Hill

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Discussion Overview

The discussion revolves around a scenario involving a person and their dog running up and down a hill that is a mile long. Participants explore the distances traveled by both the person and the dog, considering various interpretations of the hill's dimensions and the dog's speed relative to the person.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant calculates that the dog runs a total of 4/3 miles, considering the distances traveled while meeting the person and returning to the bottom.
  • Another participant suggests that the distance the dog runs depends on the hill's height and questions the assumptions made about the hill's shape.
  • A different viewpoint claims that if the hill is one mile long horizontally, the dog may travel a total of 1.5 miles, depending on the hill's configuration.
  • One participant humorously states that the dog has traveled 9 1/3 miles, introducing the concept of "dog miles," which is met with confusion by others.
  • There is a suggestion that the hill's height significantly affects the distance traveled, indicating a lack of sufficient information to arrive at a definitive answer.
  • Some participants engage in light-hearted banter about "dog miles" and other humorous concepts related to pets.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the distances traveled by the dog, with no consensus reached on the correct interpretation of the problem or the calculations involved.

Contextual Notes

Participants highlight the ambiguity in the problem, particularly regarding the hill's height and shape, which affects the calculations. There are also references to humorous interpretations of "dog miles" that complicate the discussion.

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You and your dog run up a hill that is a mile long. Your dog runs half as fast as you. When you reach the top you immediately head back down. When you meet your dog, on your way down, he turns to follow you to the bottom. When your dog reaches the bottom, how far has he run?
 
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4/3 miles. You run up the hill (one mile) and one third of a mile back down, for a total of 4/3 of a mile while the dog runs the 2/3 miles to meet you. Then the dog retraces his steps to the bottom. If he continues to run half as fast as you, when you reach the bottom he will have run one mile in total, but, after you wait for him to get back to the bottom, he will have run one-and-one-third, that is 4/3 miles.
 
Depends entirely on where the crest of the hill is...
 
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If the hill is one mile long, won't that make it 1/2 mile for each side. Secondly, assuming that its a 1/2 mile up each side exactly, then...


The dog goes up 1/4 mile, while you go up 1/2 mile

the dog then goes up 1/12 mile, while you go down 1/6 mile

then your dog goes the following 1/3 mile down, therefore, you travel 1 mile, while your dog travels 2/3 mile.

IF HOWEVER, THE HILL IS ONE MILE LONG HORIZONTALLY, THEN WE HAVE A WHOLE NOTHER PROBLEM ON OUR HANDS.

Also, if the hill is one mile long each side, then the dog travels a total of 1 1/2 miles.
 
d(dog) = 2*[(1/2) + (1/3)*(1/2)] = 2*[(1/2) + (1/6)] = 4/3 miles...but since this is a brain teaser, there's probably a catch somewhere ! [/color]
 
hmm seems easy heh

::the dog went 1.333333 miles.::
 
The hill is entirely irrelevant.


The dog has traveled 9 1/3 miles. (That's dog miles! :D )
 
What the hell are dog miles?
 
Further to my earlier point- It also depends on the height of the hill. traveling up a hill 100m high and a mile long covers much less distance than a hill 500m high and the same length.
There simply isn't enough information to give an answer.
 
  • #10
noticeably FAT,
dog miles are smaller than human miles (not sure of the exact ratio). my dog thinks dog miles are too long so we use ant miles.


my dog also feels old so we use turtle years for his age.
 
  • #11
bjr_jyd15 said:
noticeably FAT,
dog miles are smaller than human miles (not sure of the exact ratio). my dog thinks dog miles are too long so we use ant miles.


my dog also feels old so we use turtle years for his age.
Bah, does your dog use makeup to make itself look younger?
 
  • #12
Noticeably FAT, you know I'm against using makeup on animals...but in this case I make a special consideration. He likes looking in the mirror at himself--so selfish!
 
  • #13
A mile and a third right?
 

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