So they decided to start at the Greenwich Observatory in England and divide the world into 24 slices vertically, each of which is about 15° longitude wide and corresponds to one hour of time.
Because time zones are based on degrees of longitude (which are 360 imaginary lines running vertically around the planet from the North Pole to the South Pole) the distance between them changes as you move towards or away from the equator.
You sometimes forget this fact when you look at a flat map. But the earth is round, and if you could wrap that map around a ball you'd see that the lines of longitude get closer together as you travel toward the poles.
So the answer to your question depends on how far north or south you are. If you in any city near the equator, like Nairobi, Kenya, each time zone is about 1,035 miles wide. But if you're at somewhere more north like Winnepeg, Canada, the time zone would only be about 675 miles wide.