# Mile hill

1. Nov 19, 2004

### nnnnnnnn

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?

2. Nov 19, 2004

### ceptimus

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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.

3. Nov 19, 2004

### matthyaouw

Depends entirely on where the crest of the hill is...

4. Nov 21, 2004

### Noticibly F.A.T

Highlight to see

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.

5. Nov 21, 2004

### Gokul43201

Staff Emeritus
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 !

6. Nov 22, 2004

### TheHeffNerr

hmm seems easy heh

::the dog went 1.333333 miles.::

7. Nov 25, 2004

### DaveC426913

The hill is entirely irrelevant.

The dog has travelled 9 1/3 miles. (That's dog miles! :D )

8. Nov 26, 2004

### Noticibly F.A.T

What the hell are dog miles???

9. Nov 26, 2004

### matthyaouw

Further to my earlier point- It also depends on the hight 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. Nov 26, 2004

### bjr_jyd15

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. Nov 30, 2004

### Noticibly F.A.T

Bah, does your dog use makeup to make its self look younger???

12. Nov 30, 2004

### bjr_jyd15

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. Dec 9, 2004

### franznietzsche

A mile and a third right?