The faucet is clogged
No, too high of water pressure causes problems.
Replace the tub faucet.
form_title= Bathtub Drain form_header= Fix your bathtub with help from experts. When did your drain stop working?*= _ [50] Does that bathtub drain empty water too slowly?*= () Yes () No Do you own or rent your home?*= () Own () Rent
A clogged aerator on the end of the faucet would cause the water flow to decrease in that faucet.
Possibly a pressure reducing valve installed after piping for first faucet, which would cause situation describing.
check for leaks
You should purge all your water pipes of built in sediment. Don't forget, you are drinking the water too!
mostly because of rust deposits
Yes, you certainly do.
The mains water has probably been turned off and turning on the tub has drained the tank.
Could be the washer vibrating in the bath faucet/mixer. Over time, washers can degrade and become floppy or develop a rough surface. High pressure water over the surface can act like air past a clarinet reed. Opening the sink faucet takes the water feed pressure off the bath faucet, stopping the vibration.
Unscrew the aerator from the end of the faucet where the water comes out and clean the screen. Sediment build up slows the flow.