I2C at a distance

I have seven Arduinos: one by my computer, and six of them 50 feet / 15 meters away. I'd like to use the Arduino by my computer to communicate with the Arduinos at a distance.

I was planning on sending power and I2C over a CAT-5 cable (~.19 ohm/meter, or 2.8 ohms total, or if I use each of the 4 twisted pairs as "one" cable, 1.4 ohms).

Has anyone done this before? Do you need to amplify the I2C signal on the master side? Using the Wire library, can you manually lower the I2C datarate to increase the range? Is there anything else I need to know?

I2C standard was never designed to support run lengths that you wishing for. They were mostly designed to communicate with chips on the same board or possible within the same backplane system. However the good news is that there are I2C buss buffer chips avalible to make it possible to have longer runs. Check out this data sheet for ideas and suggestions and good practices.