The speed in which they can travel in spaceships seems way higher than lightspeed, despite it being stated in one episode that their spaceship can only travel up to 99% of the speed of light.

For example, in one episode they manage to get to the frontier of the universe in approximately a week and in other episode they also reach the limit of the universe as they are sent to an invented planted that doesn't really exist inside the universe.

It's also obvious that the action is supposed to be happening in our universe in the future, the facts that confirm that it's huge.

I haven't watched all episodes, so maybe in one it's explained that's it's via wormholes or something like that.

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    VTC: Futurama... – KutuluMike Dec 1 '16 at 21:42
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    Like most science-fiction spaceships, they travel at the speed of Plot. – Mark Dec 1 '16 at 22:12
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    "It's also obvious that the action is supposed to be happening in our universe in the future" ... *looks at hand* Hmm. *counts fingers* 1, 2, 3, 4... 5. I have 5 fingers on each hand. Fry and all the other humans of his time have 4. Futurama is not happening in our universe. – Schwern Dec 2 '16 at 3:12
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    It's the future... they use Future Tech™ – Toby Dec 2 '16 at 10:59
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    It's a comedy cartoon. It's not supposed to be scientifically accurate. – Lightness Races in Orbit Dec 2 '16 at 12:35

Per "A Clone of My Own"

Farnsworth: These are the dark matter engines I invented. They allow my starship to travel between galaxies in mere hours.

Cubert: That's impossible. You can't go faster than the speed of light.

Farnsworth: Of course not. That's why scientists increased the speed of light in 2208.

This neatly explains why the ship is able to travel at 99% of the speed of light, yet still able to reach distant galaxies in mere hours.

Leela: For Heaven's Gate, Professor. This ship can do 99% light speed. Why are we going 35 miles an hour?

Farnsworth: Because we're in a hurry, that's why.

Teenage Mutant Leela's Hurdles - Transcript

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    Cubert: Nothing is impossible. I understand how the engines work now. It came to me in a dream. [He lifts an access hatch and starts fiddling with some wires under the floor.] The engines don't move the ship at all. The ship stays where it is and the engines move the universe around it. ---- the planet express is unique in this i believe. – Himarm Dec 1 '16 at 21:36
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    @Himarm - That sounds like weapons-grade Balonium to me. – Valorum Dec 1 '16 at 21:37
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    Nothing is impossible, not if you can imagine it, that's what being a scientist is all about - One of my favorite Futurama quotes. Knowing that the show was written by a bunch of scientists and PhD's makes this quote all the more powerful. Also, the entire show is worth a rewatch with the directors commentary, in which they discuss things such as how the ship moves so fast, amongst many other aspects of the show, they tried very hard to make everything at least theoretically possible! – JMK Dec 2 '16 at 14:53
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    Just to briefly note, it's mentioned in the DVD commentary that they decided to go with "increasing the speed of light" as opposed to "FTL travel" because the two concepts are equally absurd but at least their version is a different absurd than what everyone else does. – MikeTheLiar Dec 2 '16 at 18:44
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    @Daevin - I think you'll find that the underlying theoretical basis for that technology is that you somehow create matter with negative mass and that somehow you incorporate that with quantum gravity to make a workable physical model. The Alcubierre Drive is a cute idea because the underlying maths is sound, but the problem isn't the math, it's the part where you need stuff that doesn't exist to make it actually work in practice. – Valorum Dec 2 '16 at 22:12

By using the Dark Matter Engine

The Dark matter engine is the key to the extreme acceleration capabilities of the modern space ship.

Albert Einstein's famous statements that it would be mathematically impossible to travel faster than light seem to have held up throughout the 3rd millennia, and although in 2208 the scientific community allegedly raised the speed of light so that they could go faster, the problem that one cannot go faster than the speed of light remains.

The solution was the dark matter engine, which doesn't move the ship through the universe, but instead moves the universe around it at phenomenal speeds and is thereby able to cover incredible distances in a relatively short period of time.
—Futurama Wiki, Dark Matter Engine (link)

  • And two dark matter engines oppositely oriented? – Vial Dec 5 '16 at 0:35

The ship has dark matter engines that allow it to move faster than light. Also, remember that scientists increased the speed of light in 2208.

In the episode 'A Clone of My Own' the Professor takes Hubert outside of the ship to explain how it travels faster than light. At the end of the episode we see a demonstration of it as the space around the ship is actually moved while the ship is stationary.

It's also a mix of the 'L-unit' and dark matter reactors.

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    Of course, without the L-unit, space travel is little more than a fantasy. – Valorum Dec 1 '16 at 21:20
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    It's a very important unit. – CBredlow Dec 1 '16 at 21:21
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    Do we count lower-case L's? – Valorum Dec 1 '16 at 21:24
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    You know we don't! – CBredlow Dec 1 '16 at 21:27
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    re: this, what's worse is that I even had sufficient time to format the answer properly and edit the question... – Valorum Dec 2 '16 at 0:49

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