The title is a play on the terms "supersonic" and 'soup or salad', as one might be offered by a waiter or waitress in a restaurant.
The usual chase starts for a few seconds, until it stops for the (appropriate) Latin names: Ultra-sonicus Ad Infinitum and Nemesis Ridiculii, plus a "bonus" name for the Road Runner's beep: Beepius-beepius.
The chase then moves around mountain corners until it ends on a mountainside, with the Road Runner ducking behind a corner and leaving a cloud of dust for the coyote to run into. Wile E. rides the dust cloud all the way through the air, and finally stops to determine where he is, a question mark appearing over his head. He opens a "door" in the cloud, only to see that he is in midair, and sheepishly closes the door as the cloud disperses, and then changes his question mark of surprise to an exclamation point before the inexorable pull of gravity takes effect.
The pair pull up onto opposite outcroppings, and Wile E. attempts to pole-vault from his to his opponent's, but this causes the end of his outcropping to crumble and the coyote to fall down. Seeing his impending humiliation approaching, Wile E. attempts to make the best of it by climbing up the pole; however, he keeps falling back to the bottom of it. Eventually, the pole turns around so fast that it whirs like a propeller, and then grinds against a cliffside all the way down to the part Wile E. is holding. When it finally stops rotating, the coyote then pulls himself onto the narrow bar left of the pole and accepts his fate.
In a gag that sees four attempts in this cartoon, Wile E. sits on a rocket and lights the fuse, aiming towards the Road Runner on the opposite site of the chasm. (Virgil Ross animated this gag, providing distinctive ear motions.) The first attempt fails when the fuel and nosecone launch out of the rocket, leaving Wile E. sitting on an empty hull. The hull crunches down, and then Wile falls, annoyed, to the canyon floor.
As the Road Runner burns rubber on the ground roads, Wile E. is pulling back on a falling safe attached to a rope and pulley. Eventually, however, the weight overcomes him and the coyote is pulled through the pulley, removing all of his chest fur, and then down onto a see-saw as the safe lands next to him. Wile then slides off the rock face to fall into the canyon a fourth time, and is then smashed by the safe, leaving the coyote's torso thin and flat.
The second attempt at the rocket is foiled when the rocket falls out of its aim towards the Road Runner and points directly downwards before it fires, leading to an extra-speedy fifth fall.
Now, Ross animates a sequence in which Wile E. sticks a firecracker into the center hole of a Frisbee (from the Freleng Manufacturing Co.) and throws it at his nemesis, but before he releases the disc, the firecracker drops out of the hole and sizzles at Wile E's foot. The coyote doesn't notice until he puts his foot down on the firework and instinctively pulls it away just before it explodes, leaving him dazed but apparently unhurt. Wile then walks away like Charlie Chaplin, revealing behind him that his tail is on fire, unknown to him until he passes the horizon and he yelps in pain!
On his third attempt with the rocket, he lights the fuse but it burns quickly and fires successfully out from under him before he could get ready and leaves Wile floating in midair with a cloud of dust blocking his view below. Unable to see what is below him, Wile pokes his foot through the cloud and consequently suffers gravity for the sixth time, as he holds up a sign stating "GOODBYE" and then flipping to "AGAIN". (One minor glitch is the scene where he falls is a duplicate of when he fell the first time with the hull underneath him.)
To get the bird to stick, Wile leaves out a sheet of ACME Giant Fly Paper in the road and sits down on a rock, laughing at his "genius". He hears a braking noise, assumes the Road Runner has been caught, and leaps out to catch him, but instead of the Road Runner, he has caught an actual giant fly. The fly is very unhappy about being stuck on the paper and thus wraps the coyote with it, who tiptoes away from the scene.
On his final attempt at the skyrocket, Wile E. accidentally ignites his tail instead of the fuse, and detects his mistake and leaps up in pain only to smash his head on another outcropping. Fortunately, this causes him to return to the rocket and to light the fuse with his tail, and after it takes off is struggling briefly to get control then puts out the fire on his tail. Unfortunately, the rocket is off target, and it bores through the cliff under the Road Runner, who allows the coyote to be humiliated privately. The rocket finally explodes, blackening the coyote and throwing him back into the air. Displeased, Wile E. holds up a yellow sign asking "HOW DID I EVER GET INTO THIS LINE OF WORK?" before falling for a seventh time.
A new plan is formulated, where Wile E. attempts to blow up the Road Runner by pelting explosive tennis balls at him. The first ball seamlessly blows up a cactus with no issues (yet), and the coyote is eager to try them at work. As luck would have it, the Road Runner is heard, and Wile is quick to lob another ball at him, but just misses, and the ball then drops onto the arm of a cactus, which throws it directly back to its owner. A little agitated, the coyote returns the ball, and this time it is caught by power lines and slung back out of Wile E.'s reach. The ball pops directly back into its original slot in the box of balls as Wile E. arrives on the scene and takes stock. Sensing the coming explosions, Wile E. holds up a pair of signs: "For Sale One used Tennis Racket" and "CHEAP!" before (as the screen puts it) a "GIGANTIC EXPLOSION!" occurs.
The whole cartoon, however, is best known for its ending gag. Wile E. Coyote is chasing the Road Runner through a series of pipelines, which causes both of them to emerge in a greatly shrunken state. Upon discovering their situation, they agree to re-enter the pipeline and be transformed back into full size. The Road Runner emerges at normal size, but Wile is still in small size when he comes out. Upon discovering this turn of fortune, the Road Runner stops and allows his rival to "catch" him. The coyote doesn't notice anything until he steps over his opponent's legs and rushes back to finally "catch" the Road Runner. The coyote is ecstatic and pulls out his knife and fork to eat his opponent...until he stares more closely at the bird's huge legs, which are twice as tall as he is, and looks up to see he is massively outgunned. The Road Runner gives his antagonist an amplified "beep-beep", causing Wile to drop his utensils in shock. He can only hold up signs to the audience stating, "OK, wise guys - you always wanted me to catch him -" "Now what do I do?"
This was the only Looney Tunes cartoon short where Wile E. Coyote ever caught the Road Runner. However, in The Looney Tunes Show, Wile E. Coyote caught the Road Runner twice.
A unique opening card was used, however, the closing card was from the 1959-64 season.