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Dwight BaerFlag for Canada

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What is the optimal length of Cat 6 Ethernet cable before the signal starts to degrade?

I need to build a wired network to a distance of 1000 metres (3000 feet).  This is as an alternative to a TrangoBroadband wireless solution which is quite expensive.  My intention is to "daisy-chain" 10 lengths of 100-metre Cat 6 Ethernet cable, joined together by switches.
My question is, "What is the optimal length of each of my segments?"  Assumption:  At the end of the exercise I want the best signal (in the building which is 1000 metres away from the source) at the lowest price.  Should I truly plan to install 10 segments (joined by 10 switches) or would I get a better result, for example, if I installed 20 segments, each 50 metres long, joined by 20 switches?  Thanks.
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Hmmm... Fibre is scary to me.  I live in a remote community and it would involve flying in expensive help.
I found this link:  http://www.ferret.com.au/articles/z1/view.asp?id=90396

I think I'm safer if I make my segments something less than 90 metres, and not more than 5 segments altogether, meaning a total distance of 5 x 90 = 450 metres.

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Thank you everyone.  

Summary so far, including two supplementary questions:  
1.  I think I'll try to restrict my segments to 90 metres long if it's practical.  But I've read about lots of people who have used 150-metre segments successfully (probably with light traffic).  I even read about somebody who put ends on a 1000-foot (330-metre) box of cable, and successfully made a connection.
2.  But I still don't know how many segments is worth trying.  2 or 3 segments joined by switches?  Yes, absolutely it would work.  5 segments?  Maybe there'd be a lot of collisions.  So it would work with light traffic but might produce a lot of errors with heavy traffic.  (Actually I should have said that as a question, not a statement.)  10 segments?  (This was my original question).  Nobody yet has even ventured to think it might be possible.
3.  It seems to be clear that a network operating at 10 mbps can have a greater network diameter than one operating at 100 or 1000 mbps.  My switches have the capability of 10, 100 or 1000 mbps.  (The light is orange when it's 100 mbps, or green when it's 1000 mbps.)  
4.  But what I don't yet know is:  If these switches start encountering a lot of collisions during heavy traffic, are they smart enough to switch down automatically to 100 mbps or even 10 mbps, in order to reduce the errors?  If the answer to this is yes, then clearly I can install a 10-segment network (i.e. a 900-metre network diameter), as long as the customer understands that his performance at the far end will be slow.

So my new questions are:  

1.  Can somebody venture a guess about whether as a businessman I should implement a solution that includes up to 10 segments (900 metres)?
2.  Can somebody clarify for sure that my 10/100/1000 mbps switches will automatically lower their transmission speed if they start to encounter errors due to packet collisions?