What's wrong with my wifi network?

Question

I recently upgraded my internet from DSL to Comcast Wireless Gateway (cable modem + wireless router) in order to improve speed.  It has certainly done that.  My previous (DSL) download speed was approximately 2.5Mbps.  Now it’s 54Mbps with the cable modem.
However I live in an old, 2-story house with thick plaster walls, and when I get any distance at all from my cable modem, my WiFi Signal-to-Noise goes from 70+db to 10db or less.  I’m measuring this using the Apple utility "Wifi Diagnostics".  I can walk around my house with a Macbook Air and watch the SNR change from room to room - very handy.
I understood from other forums here that I can use my Airport Extreme to extend my wireless network as long as I connect it to my Comcast Wireless Gateway (CWG) using a wired (Ethernet cable) connection.  I’ve done that.  I ran a Ethernet cable between the CWG and AE.  I configured the AE, using Airport Utility (by editing the AE settings once Airport Utility “saw” the AE) to extend the network, and gave it the same network name and password as the one I set up for the CWG.
This all seemed to work fine.  The AE shows up in Airport Utility below the “world” globe labeled, “Internet”, and it says among other things, connection: Excellent, status: Extended Network.  All good, right?
Unfortunately this configuration does not seem to have any effect on the strength of my WiFi signal.  i.e., I can place my Macbook Air within several feet of the AE (several rooms away from the CWG) and the SNR is still only about 10db. 
What's going on, what am I doing wrong?  ear in mind, I’m a complete networking novice.

Answer 1

After posting the above question, I came across the following post:  https://discussions.apple.com/message/17978428#17978428
I ended up redoing my configuration using the steps described in the post for setting up a "roaming" set of routers (repeated here):
Connect the two routers together with a long ethernet cable. If the building is prewired with data ports (ethernets cables in the wall) then use those connection points to patch over the connection between the routers. Plug one end of the cable into a LAN port of the router connected to the DSL/Cable modem, in your case the TalkTalk router. The other end of the cable is plugged into the remotely located router's WAN port, the AirPort Extreme. Plug the power into both routers.
Plug your computer's ethernet port, that has AirPort Utility software installed on it, into the remote router's LAN port using an ethernet cable.
Open AirPort Utility from the Applications>Utility folder.
Select your AirPort Extreme base station and then the edit button on the balloon window that pops up.
Select the Wireless tab
Set the Network Mode to "Create a wireless network"
Set the Wireless Network Name to the same name as the existing wireless network using the same letter case used on that network. This is also called the SSID in some routers.
Set the Wireless Security and Wireless Password to be the same as the existing wireless network.
Select the Network tab
Set the Router Mode to Off(Bridge Mode)
Select Update
After completing these steps I unplugged my Airport Extreme from my computer, unplugged power, and moved it to a remote location (still connected to my Comcast Wireless Gateway with an ethernet cable).  I plugged it into AC power, waited for the green light, and then tested my wi-fi signal-to-noise ratio with the Apple "Wi-Fi Diagnostics" utility.  As I walked toward the Airport Extreme with my Macbook Air I could watch the SNR increase to 40-50 db.  So, now working as I had hoped.