At what time was Jesus crucified?

Both Mark and John indicate the approximate time at which Jesus was crucified. Unfortunately, their accounts don’t agree on when this was.

The Jews measured time by counting the hours from dawn (roughly 6am). The third hour was thus about 9am, the fourth hour about 10am, and so on.

Mark gives the time of the crucifixion as the “third hour”, helpfully translated by the NRSV as “nine o’clock in the morning”:

It was nine o’clock in the morning when they crucified him. [Mark 15:25 (NRSV)]

According to John, it wasn’t until the sixth hour (or “noon” in the NRSV) that Pilate handed Jesus over to be crucified, suggesting that Jesus was crucified some time after midday:

Now it was the day of Preparation for the Passover; and it was about noon. He said to the Jews, ‘Here is your King!’ They cried out, ‘Away with him! Away with him! Crucify him!’ Pilate asked them, ‘Shall I crucify your King?’ The chief priests answered, ‘We have no king but the emperor.’ Then he handed him over to them to be crucified. [John 19:14-16a (NRSV)]

The only other indication of the time of the crucifixion we get is in Luke. Luke describes the crowd mocking Jesus on the cross, and then says that a darkness fell from 12 noon to 3pm:

It was now about noon, and darkness came over the whole land until three in the afternoon… [Luke 23:44 (NRSV)]

As in this account Jesus is already on the cross when the darkness falls, Luke’s timing seems to fit with Mark’s and conflict with John’s.

So at what time was Jesus crucified, at 9am or some time after noon?