This is a supplement, NOT a replacement to the well-researched and thorough answer from Meyer, above...
In my washing machine, the hard water deposits blocked up the inlet quite a bit, to the point where it appeared to be failing.
I bought a $10 bottle of CLR, or "Calcium/Lime/Rust," sold in a usually gray bottle and ran the roughly 1/4-gallon container through a warm cycle twice, half of the bottle each time. It cleared out the hard water, and the inlet ran well afterwards.
Twice a year, I use CLR the same way on my dishwasher and soak my shower head in it to remove minerals and hard water buildup. CLR is essential for anyone's cleaning "kit" where water is used-- the sink, bathtub, etc.
Remember, Meyer's post is VERY complete and *most likely* your problem with a slow inlet.
NOTE: On the first cycle, with the CLR in the clothing washer, let the water fill up and sit with water/CLR in it for at least a couple of hours. Also, CHECK YOUR MANUAL to make sure there isn't any reason NOT to use CLR on it... I can't think of any, but I'm not an expert on washing machines.