This can be caused by a faulty or worn fill-valve diaphragm. It must be replaced. Keep in mind that if you find it difficult to find the proper parts for the ballcock, it is easy and inexpensive to replace the entire valve.
This is the ballcock (or one much like it) found in most American Standard toilets made in the last decade or so.If you are careful when replacing parts of this valve it will last many years with just a few repairs costing a dollar or two each. All of the adjustments and repairable parts are at the top. Because the float arm is plastic and cannot be bent, a large nut that can be loosened by hand is integrated into the float rod so you can adjust the water level in the tank. Make level adjusments with the water turned off! There is one adjustment screw at the top of the float rod assembly near 'A' that is used for setting how far the float ball will drop when the toilet is flushed.
Be sure not to let the float go down too far because the flush actuator will become hung-up on the float. One or two trial flushes will show you where it should be. To replace the diphragm and plunger inside the ballcock, remove the screws around the top of the unit near 'A' and lift these parts out. Watch how they come out and you will be able to install the new ones easily. To replace the ballcock completely, drain the tank till dry, disconnect the water line connection to the bottom of the tank, and then undo the nut from the underside of the tank while holding the ballcock steady with the other hand. If you count on the float rod to hold the ballcock from turning inside the tank, it will break. It's as simple as that!. Install the float rod to the new ballcock before tightening the new unit in place. This way you can see exactly which way it should point. Another possible reason why the toilet tank takes a long time to refill is that the tap leading into the tank is not fully open or is blocked by some other cause.