We have a pretty standard washer set up (in photo). We’d like to add a utility sink so that we’re not washing paint brushes and such in the kitchen sink. Can we add splitters at the hot and cold water taps, to have water going to both the washer and the sink? And then, drain the washer into the sink and have a similar hose coming out of the utility sink drain and running into the drain pipe in the wall? Or is this a much bigger task than I’m thinking?