Generally, a Motion to Adjust is quicker than a petition. It can take a month or less.
How long a Petition to Modify Child Support Order takes will depend in part on the county you are filing in, if the other parent lives in Washington, and how you have your court papers served on them. The other parent will have anywhere from 20 to 90 days after being served to respond to your petition.
If the other parent does not respond in time, you can ask the court to enter final orders by default. If you follow the procedure correctly, it will save you time. If you do not follow the procedure correctly, the other parent could later ask the court to cancel the order.
If the other parent responds, how long it takes to finalize the case will vary. It may take at least 2 to 3 months to finalize.