I have a digest with a similar story in it, though I can't find it at the moment. The story is from the 50s or 60s and I believe the art is by Harry Lucey. Archie and Reggie are trying to outdo one another when Miss Grundy asks someone to wash the blackboard. Reggie ends up tripping Archie (I believe), causing him to get mad. He picks up a book and flings it at Reggie, who ducks, causing the book to hit Moose instead. Meanwhile, Jughead walks into the room with a box of poster paints, slips on the water on the floor and spills some of the paint on Betty, Veronica and Ethel. So now everyone is chasing after Reggie and Archie, while Miss Grundy and Mr. Weatherbee make some smart-alecky comment on the situation.

I'll look around over the coming days and see if I can find that story.

Found that story. It's called "Clean Slate" and is towards the back of a recent issue of Archie Double Digest (the one featuring Archie standing there with a big goofy hat and oversized sunglasses on while eating a popsicle).

The story line goes like this:
Miss Grundy asks for volunteers to wash the blackboard.
Both Reggie and Archie volunteer, and Archie rushes to get the water before Reggie can.
Archie rushes to the blackboard with his pan of water, claiming he's the champ at washing blackboards.
Reggie trips Archie, causing him to splash water all over Veronica.
Veronica, angered at getting soaked and having her hair ruined, picks up the pan and flings it at Archie.
Archie ducks, causing the pan to hit Reggie instead.
Reggie picks up his book and flings it at Archie, who ducks again, and the book hits Moose.
Moose gets up and chases after Reggie.
At this time, Jughead is seen walking in the door with a box containing several jars of red poster paint.
Reggie and Moose crash into Jughead, sending the paint flying. A couple of jars crash on Betty and Ethel's desks, causing paint to land all over them.
Mr. Weatherbee comes in to see what the ruckus is about, and Miss Grundy comments that you'd think someone could invent a blackboard that could wash itself, as Archie is seen running off with Betty, Ethel and Veronica hot on his tail.

By far one of the funniest stories I've seen in a long time, with great artwork from Harry Lucey.