bladder tank pressure drops quickly as water is running
Could be the tank is a bit small for the system; we try to avoid cycle times of less than a minute. Could be there's a problem. If this is a significant change in behavior from previous behavior, likely a problem; if you never paid attention before, it could be the way it's always been.

Diagnostic step one. Turn off power to the pump, drain water from the system (WATER pressure gauge should read 0) and check AIR pressure in tank.

For a system set at 40-60 PSI as you described, air pressure in the bladder with no water pressure should be about 37-38 PSI. Adjust if needed. If it's also 0, or won't stay where you adjust it to, the bladder has failed and you need a new tank (or bladder, but replaceable bladders often don't cost less than a new tank. Economics is weird. In one case I had, the price was almost exactly the same, but a new bladder had no warranty and the joy of getting the old one out and the new one in, while a new tank had a 5-year warranty...)

Then power up the pump and let the system run until it shuts off. Without using water elsewhere, fill buckets or other known volume items JUST until the pump kicks on. Record the volume that took, and you have some actual diagnostic information. You should be able to look up the specifications of your tank and determine whether the volume you "drew down" matches the expected "draw-down" volume of your tank for 40-60 PSI. If it does, it's working as expected; but you should probably double the tank size to meet the standard aiming point of a minute or more between pump starts. 

Another possible mitigating approach (if the bladder is intact and the tank is too small) would be to lower the pressure to 30-50 (set tank 27-28) or 20-40 (set tank to 17-18) which will store more water in the tank (really, look at the charts for your tank, they will tell you.) That assumes your pressure switch is adjustable (be extra certain the BREAKER for the well is off before opening the pressure switch to adjust it, if you do. It has power when the pump is not running.)