After an initial period of confusion, the four travellers find they have been transported forward in time to just before the end of the universe. They are in Milliways, the Restaurant at the End of the Universe, which was built on the ruins of Magrathea. So, as Arthur says, they have travelled through time but not through space. Waiting for them is Marvin the depressed robot, whom they left on Magrathea 40 million years ago. He's now an attendant at the car park, and still depressed.
Just before the universe ends, Zaphod and Ford get Marvin to help them steal a supercool all-black spaceship, which turns out to be the property of a very loud rock band called Disaster Area. The episode ends on the cliff-hanger as the black ship is about to start a dive into the sun of Kakrafoon.