Really simple Router question.?

[squarecan470]

My computer that I bought 1.5 years ago has a great Wi-Fi connection, even though it is wireless. But sometimes, my internet connection just goes to shit. My brother has a computer hooked up to the router and modem about 8 meters away, and so I bought a newer router that I know is faster and also runs on 2.4GHz and 5GHz.

My question is, since I have a computer that connects to a router wirelessly, can I plug the new router into it and have it still work? Or do I replace the new router with the old one and keep it at my brother's computer?

Other info:
(My main problem with my internet connection at the moment is losing connection whenever someone talks on the phone as well as losing speed at random times.)