Water tank problems

2 problems have recently started with my hot water tank.
1. Every time we have a bath and the tank fills up it starts to drip from the overflow. Running the hot tap for a minute or 2 causes it to stop. 2. At the same time this started I also noticed that I dont get as much hot water into the bath until it starts to run cold.
I seem to remember one time someone told me your tank can start to fill with dirt in the bottom of it. Is this the problem and is it a case of removing the element and scooping out the dirt on the base of the tank. Its awkward because its up high on the wall of the bathroom but I replaced the element about 10-15 years ago so I can do it ok!
Or is the water running cold too soon simply a case of a new element reqd? I always thought they just stopped dead and dont remember the water getting gradually colder in this manner.
Any help or ideas appreciated!
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