Another patchy WiFi question thread

Greetings

Currently we have a white orcon Genius router/modem thingie, in the middle of the house, but the signal barely reaches the lounge, i do have ethernet cable running under the house to an ethernet switch in the lounge which provides ethernet for a couple of computers etc but of course it doesn't help with the wifi.

i was thinking of using one of these

Apple airport extreme doohickeys as they seem to be small discrete and to do the exact job I want.

Obviously it will get its feed from the ethernet cable, so the WiFi it puts out will that be a separate wifi network or can it be configured to be the same as the existing one, or am I completely missing the point here.

I had previously a few years ago tried to turn an old router into a wifi extender, but for some weird reason some devices would hang on to the signal from that and not go for the signal from the genius router even when down the other end of the house where the old router signal didn't reach.