In 4/4 time, how long is an eighth note played?

Half a beat

Explanation:
4/4 time (aka Common time) can be defined as 4 beats per measure, with the quarter note receiving one beat per measure. In common time, a sixteenth note is 1/4 of a beat(as there are 16 sixteenth notes in a measure in common time), an eighth note is 1/2 a beat(8 eighth notes can fit in a measure in common time), and a quarter note is one beat(with 4 beats a measure in common time). Keep in mind that the note name is corresponding to the number of those notes in a measure in common time, as shown above. An eighth note has 8 of its notes per measure in common time, and because common time has 4 beats a measure, 4 beats divided by the 8 eighth notes show a note value of 1/2 a beat for each eighth note.