I turn on the hot water tap for my bathtub, giving it maybe half a
turn, leaving it until the water is hot. I then turn on the cold water
tap, and only have to turn it a fraction of an inch or so before the
water is warm. If I turned it as much as the hot water tap, the water
wouldn't even be warm, it would be cold. What is the problem and how
can I fix it? (It's been like this for ages, and the distance you have
to turn the cold water tap before the temperature is optimum is
getting less and less.)

Let's look at some hypothetical data. Assume your hot water is at 130F,
your cold water is at 45F, and your desired temperature after mixing is
110F. Further assume that both knobs allow the same amount of water to
flow through when opened the same amount and each allows 2 gallons per
minute (GPM) flow when fully open.

Open the hot knob half way. You now have 1 GPM at 130F.
Open the cold knob half way. You now have 2 GPM at (130+45)/2 =
87.5F--way too cold.

Although the physics is probably not this simple, you can see that
you'll never get the temperature you want by opening both valves
similar amounts.

Others have pointed out that physical conditions in your water system
can effect the temperature, maybe more than the mixing temperatures.

I would start by replacing the washers. It's easy and cheap, and it
probably needs to be done anyway. Maybe it'll help, maybe not, but
you'll be out less than a buck.

--
Steve Bell
New Life Home Improvement
Arlington, TX USA