Old home water systems sometimes start filling up with sediment after years, with the water stream notably diminished. It's no coincidence that it's usually the hot water that's running slowest. The heat in the water can cause minerals and debris to coalesce and get stuck on the inner sides of the lines. There is an old plumber's trick for "backflushing" your system--essentially, running cold water backward through the hot water lines to loosen all that sediment, then expelling it at a low faucet.
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Go to your water heater and locate the water pipe that feeds into it from the top. The pipe will feel cold to the touch, indicating it is the incoming water (the other pipe on top, which carries the water out of the heater, will feel warm). Trace the cold incoming pipe back to the first valve you find. Turn it off, cutting the water supply to the water heater.
Go to the lowest faucet in your home, preferably in the basement. Turn on the hot water tap. Nothing should come out, since the hot water feed is turned off. (It may expel built-up hot water for a minute or two before it runs dry.)
Go to one of the slow faucets. Take off the aerator screen from the end of the faucet by turning it clockwise (the opposite direction you would turn to unscrew a screw). Press a dime into the screen, blocking it. Screw it back onto the faucet, turning it counter-clockwise to tighten it.
Turn on the hot water tap, then turn on the cold water tap. No water will come out (because the dime is blocking it), so the cold water will run back through the hot water line and out the open hot water tap in the basement.
Observe the basement tap for gunky, debris-laden water coming out. When it runs clear, go back to the upstairs tap, turn everything off, take the dime out of the aerator, and proceed to the next slow faucet. Repeat until you've backflushed each line to each faucet in the house, then turn off the basement tap and turn on the water line to the water heater.