# Brain Teasers Help

1. Oct 5, 2004

### lrandf

Please someone help me with these brain teasers, Thanks! I have try to answer these problem, but I don't know whether they are right or wrong. PLEASE HELP!!!!

A hill is one mile from the bottom to the top and then one mile from the top to thebottom. A person drives a car from the bottom to the top going 30 MPH. How fast does the person have to drive the car down the hill inorder to average 60 MPH fro the entire trip?

There are four volumes of Shakespeare on the shelf. The pages of each volue are exactly two incles thick. The covers are each one-sixth of an inch thick. A bookworm started eating at page 1 of Volume I and ate straight through to the last page of Volume IV. What distance did the worm cover?

Ann

2. Oct 5, 2004

### kazimo

I think those are the right answers.

For the first one the calculations are something like (30+x)/2 = 60

So according to that x ( the speed that she would have to go down the hill ) is 90 mph.

For the second one the worm eats through 6 covers ( 2 on each side of the 4 volumes minus the 2 covers of the first and last volumes ) and 4 sets of pages.

So the total distance would be ( 6*1/6)+ (4*2) = 9

Last edited: Oct 5, 2004
3. Oct 5, 2004

### Gokul43201

Staff Emeritus

The second answer is smaller than 8 inches...try it and see.

4. Oct 6, 2004

### hemmul

huh! the person has to drive REALLY REALLY REALLY very fast!!! but according to STR, he won't be on time, though :)

spoiler with the white:

there two equal parts of the road: first and second, both of length L.
The first part takes the time of: t1=L/v1,
while the second: t2=L/v2. We have to calculate v2.
As the mean velocity is vmean => vmean=2L/(t1+t2)
Thus: v2=1/(2/vmean-1/v1). in our case v2=oo

5. Oct 6, 2004

### hemmul

how are those books standing?
if like this:
[1][2][3][4] then the answer is not only < 8 (as Gokul wrote), but also < 5 :)

6. Oct 6, 2004

### Gokul43201

Staff Emeritus
Hemmul, you reveal too much (but I disagree with you that it's < 5. Did you mean <= 5 ?) ! I think these problems were actually homework, this is a double-posted thread.

Last edited: Oct 6, 2004
7. Oct 6, 2004

### hemmul

actually - yes :) i wanted to write something like <5.0001... but decided that it will do...
argh... i really don't watch for double-postings... probably it's already too late to delete my posts, so i'll just take into the account "homework questions" for future

8. Oct 9, 2004

### Moonbear

Staff Emeritus
Ha ha...if it's anything like my bookshelf, they are stacked like this:
_
1
=
2
=
3
=
4

In which case Kazimo got it right. :rofl:

9. Oct 9, 2004

### Gokul43201

Staff Emeritus
But not if they are stacked like this:
_
4
=
3
=
2
=
1

My bookshelves have a combination of horizontal (the majority) and vertical (when I get lazy) stacks.

10. Oct 11, 2004

### NoTime

Don't forget the mile up and down totals 2 miles :surprised

11. Oct 12, 2004

### SplinterIon

Sorry if I appear slow - but how would that equal 5 inches if it is [1][2][3][4]
To eat through the pages of 1,2,3,4 is 8 inches. To eat through the covers is 1 which makes 9.

Huh??!?!?!?!? What am I missing?

**Sorry - I just reread the question and realized where I went wrong. My case would only apply if we stacked our books back to front.**

Last edited: Oct 12, 2004
12. Oct 12, 2004

### Gokul43201

Staff Emeritus
You're missing where the first page of [1] and the last page of [4] are located.

If you actually tried this with books, you'll have no trouble seeing this.