Does a wireless repeater slow things down for everyone?
Solution 1:
A wireless repeater is slower for those connecting to the network using it. This is because it uses the same radio to accept incoming and outgoing packets from clients as it does to forward those packets on to the next wifi router and accept replies.
So effectively you get half the bandwidth, as each packet must go over the air twice - from the client to the repeater, then from the repeater to the wifi router.
It will not affect anyone directly connected to the original wifi router (other than from having to share it among more people).
If you are in range of the wifi router and so connect to it rather than the repeater, you will get normal performance.