I have always heard that Jesus encountered the woman at the well (John 4) at noon because a woman of her reputation (John 4:17-18) would go at time when other women did not go. That also seems to be the majority opinion by Bible Commentators on this passage. However, I believe that John uses Roman (modern) time whereas the other gospel writers use Jewish time with the hours beginning at 6:00. Historically, water-drawing took place either in the early morning or at dusk in order to avoid the Mediterranean heat. So 6:00 in the evening is more likely than noon. The disciples had gone into the village to buy food. According to Josephus, the Jewish historian, the main meal of the day was eaten in the evening, usually a little before and after sunset, before it became pitch dark. Then John 1:39 says that John and Andrew “saw where He was staying, and remained with Him that day (now it was about the tenth hour).” Nothing conclusive here, but 10:00 in the morning is more likely than 4:00 in the afternoon for that memorable extended encounter with Jesus (“remained that day.”) Then John 19:14 is the most conclusive. It says, “Now it was the Preparation Day of the Passover, and about the sixth hour. And he said to the Jews, ‘Behold your King!’” Note that Pilate's presentation of Jesus for judgment before the crowd took place at the 6th hour. That had to be 6:00 in the morning rather than noon (cf. Mk. 15:25, 33-34). Another example is 4:52. At the “seventh hour” the nobleman’s son was healed from a distance by the word of Jesus, 7:00 p.m., which would explain why it was not until the next day that the nobleman traveled the 20-25 mile journey from Cana to Capernaum and discovered the good news." Another reason why John uses Roman time and the other gospels used Jewish time is became the other gospels were written when Judea was still a nation, plus we would expect Matthew, written to the Jews, would have used their time. However, John was written 20-25 years after the destruction of the Jewish nation, and by that time the church had become majority Gentile. I consider it likely that John 4 took place in the late spring or early summer, when it did not get dark until about 8 p.m.