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Puzzler

 
 
Reply Wed 9 Mar, 2005 05:34 pm
At 8:00 am, you leave your car and hike into the woods. Six hours and five miles later you stop to make camp. The next morning, you leave at 7:00am and hike back to the car. I claim there is a time T during the hike back at which you are at the same spot on the path as on the previous day's hike out at time T. How can I be so sure???
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Type: Discussion • Score: 1 • Views: 765 • Replies: 6
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raprap
 
  1  
Reply Wed 9 Mar, 2005 08:40 pm
Assume a constant walking speed (v mi/hr)

The distance from the car to the camp is
D=6v+5 mi

The crossing point is d miles out and (D-d) miles back

At a constant walking speed
d=vt
where t is the walking time from a start at 8:00 AM

and (D-d)=v(t+1)
t+1 is because you started an hour earlier on the way back

Since D=d+(D-d)=vt+v(t+1)=2vt+v
and D=6v+5

then
6v+5=2vt+v

separate and solve for t

then t=5(v+1)/2v=5/2(v+1)/v=5/2(1+1/v)

So you can't solve for t without knowing the walking speed. However; if your walking speed (v) is 3mph then

t=5/2x(1+1/3)=10/3=3:20 (3 and a third hrs)

So if you walk at 3mph on the way out and back you'll get to d at 11:20AM.

at 2mph its 15/4=3:45+8:00=11:45AM

at 1mph its 10/2=5:00+8:00=1pm

Rap
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markr
 
  1  
Reply Wed 9 Mar, 2005 09:53 pm
If you get back before 8:00 am, then what you claim won't happen.

An easy way to be sure, is to consider two hikers hiking on the same day. One leaves the car at 8:00 am, and the other leaves camp at 7:00 am. They have to meet on the way (subject to my opening statement).
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rockerpham
 
  1  
Reply Thu 10 Mar, 2005 12:15 am
My teacher said that the answer is really really short ('cause this is a puzzler). The answer is about 3 sentences. So I think mark's way could be right. Smile
It's so funny. I have thought about it for 1 week but I can not find the answer Laughing
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rockerpham
 
  1  
Reply Thu 10 Mar, 2005 12:35 am
I have another one Very Happy
If 2 people play a game.
Its rule is:
You put a can (beer, coke or so on) on a table (circle).
(You could put anywhere)
Then your opponent puts another can on that table. (could put anywhere)
You put another one. Then comes your opponent's turn.
It's continue until one people put the last can on that table. Then there is no space to put anymore can. The one who put the last can will win the game.
So to win that game, should you be the first one put the can down or let your opponent put the first can? (the size of the table does not matter)
You can only put the cans down, then you're not allowed to move it.
Just put it down. That's all.
It could be some space between two cans, but that space is not enough to put one can between them.
The answer is about 2-3 sentences.
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markr
 
  1  
Reply Thu 10 Mar, 2005 10:21 am
Place your can in the center of the table, then mirror every move your opponent makes. You're guaranteed to have a move if your opponent does.
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rockerpham
 
  1  
Reply Thu 10 Mar, 2005 11:28 am
Good idea markr!
Thank you so much.
0 Replies
 
 

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