Washing a rug is easy when it's hot outside. Just pull the rug on the driveway, turn on the hose, and let the kids play in the water! It works even better when you give them scrub brushes and a broom to use as water toys!
After the rug is sufficiently soaked, (make sure to turn off the water so it doesn't look like you are watering the driveway) see who can "squeegee" the most water off the rug using a variety of plastic lids, brooms and brushes. When you are done, drape the rug over the picnic table to dry. It will be dry by dinner time!