Rusty water runs from one of our bathroom shower faucet for a little then clears.The house is about 40 years old and rented out.Instead of changing the piping of the whole house, is there a less expensive way of fixing this problem.And also does this cause any health hazzard ? Thank you.

Would this be hot or cold water that you see? What type of pipes do you have? Copper, plastic or galvanized?
Let me know, Tom

If you get a short burst of rusty water from hot and cold, then it clears up, it sounds like somebody used a black iron nipple (most likely on the tub spout). How long does it run before it clears up? I don't believe it is a health hazard, as long as you let water clear before using. Try unscrewing the tub spout and let us know what material the nipple is(make sure it is a threaded spout before trying to unthread).

Agree with MGD: it may be the spout nipple

rusty water runs from one of our bathroom shower faucet for a little then clears
Would you be talking about the tub spout? Let's clear that up. Tom

I honestly don't know what type of pipe are used but I doubt that they are copper because we haven't replaced them,they are the original.
I guess either hot or cold water is turned on it takes about 5-6 seconds of rusty water runs then clears.I tried to unscrew the tub spout but it seems like you need a special tool to do it because the distance between the tub and the spout is too little for me to use a regular screw.
If so,the problem is the spout nipple as you call... It's worth a shot to change it versus replacing the pipes in the house.How much will it cost approxiamately? And thanks again.