(We talked about this in class recently, thought I'd share.)
The speed of sound in air is around 760 mph, or 1200 kph - that's fast, but it's not terribly fast. It's fast enough so that face-to-face human communication is essentially instantaneous - if someone speaks to you from across a room, you don't see their lips move and then hear the sound a moment later. (It is fun to consider how the universe you live in might be different from time to time!) But, sound is slow enough that you see the lightning and then hear the thunder, and slow enough that you are able to hear echoes distinguished from the original sound.
Earthquakes produce two waves, the primary or "P" wave that arrives first, and the secondary or "S" wave that arrives second. The P-wave is a longitudinal wave, just like sound (meaning as it travels, it makes the material wiggle back and forth parallel to the direction the wave is traveling) - and indeed it basically is a large-amplitude, low-frequency sound wave.
(Longitudinal wave graphic by cdang, CC.)
If that wave traveled at a mere 760 mph, we would have plenty of time (depending on exactly where the earthquake was of course) to warn people it was coming. Michigan, where I live, is just about one of the least earthquake-prone locations on the planet, but by way of example, it's about 10 minutes from the capital city of Lansing to Detroit at 760 mph - plenty of time to provide the people in Lansing warning of an earthquake in Detroit, say.
Unfortunately, all else being equal, the denser the substance the faster the wave travels, since longitudinal waves propagate by particles ramming into and tugging on other particles. (Although it is interesting to know that sound travels faster in warm air than in cold air, despite warm air having a slightly lower density, and this fact often lets you hear further at night... but that's another story.) In rock, sound waves travel at something like 13,000 mph, a speed that means we can usually only give people a few seconds of warning of an impending earthquake - enough time to grab the hard hat businesses in earthquake-prone areas sometimes have on hand for their employees, or otherwise prepare yourself, but probably not enough time to leave a building.
Some countries do have such warning systems however - here is a news broadcast in Japan that is interrupted early on by a warning about a magnitude 7.4 (it turned out) earthquake that occurred just off the coast on Nov 22, 2016.
(This earthquake actually did also produce a small tsunami, and you can see the anchor get very concerned about that at the end of the video.) And below (but you'll have to click the link to see the graphic, unfortunately) there is a nice tweet visually showing the speed of this same earthquake wave as it is detected by seismograph stations in Japan, covering basically the full-extent of its travel in around a minute maximum.
［気象庁発表］
— 地震速報 (@EqAlarm) November 21, 2016
22日05時59分頃地震がありました。
震源地は福島県沖（北緯37.3度、東経141.6度、いわきの東北東60km付近）で、震源の深さは約10km、地震の規模は7.3と推定されます。
津波警報等を発表中です。 pic.twitter.com/stAvvNGXA6