There are a couple of ways to build a P-Trap for a double sink.
The usual P-Trap arrangement under a double bowl kitchen sink drains by a long pipe from the garbage disposal to the opposite sink and down into the wall drain. Recently I moved into a new home, and noticed that when the dishwasher started draining it backed up into the garbage disposal sink, leaving debris covering the bottom of the sink after it slowly drained out. If I was in the kitchen when the dishwasher started I would plunge the sink to get the water to drain faster.
I checked the drain setup and found that the dishwasher drain hose was connected to the 3/4' nipple on the upper portion of the garbage disposal, which is not uncommon. I checked for clogs, but found none. It appeared that the dishwasher was discharging water faster than the disposer could drain.
I solved the problem by purchasing a tailpiece with a dishwasher nipple, and a 3/4' plastic plug. I installed the dishwasher tailpiece below the drain basket on the opposite sink, and put the plug, with some silicone on it, into the disposal nipple, which solved the problem. The water is now draining directly into the 1-1/2" pvc drain pipe, allowing the water to flow more quickly. There haven't been any sink backups since.
The standard P-Trap doesn't work for every application; sometimes you have to make modifications to make it work properly.
