The first three gospels contain much similar material leading 'scholars' to wonder about their interdependence. Some go so far to say it is a taint on the reliability of scripture when they differ. The standard answer is that if three people witness the same traffic accident, you will get three slightly different stories.
Some speculate that the three derived content from a fourth document called 'Q'. Even with the speculation of Q, they are hard pressed to explain the source of new material, the farther away from the events.
The traffic accident theory adds nothing to assist in the interpretation of scripture. It is an excuse to ignore differences as unimportant. This cast doubt on the reliability of scripture.
The Q speculation is a direct challenge to Jesus who said that not a jot or tittle would disappear. If the Q document did exist, it certainly was not scripture.
There is a solution suggested from scripture itself. Here is a summary. Can you find the scriptures that suggest it?
1. Two men were shown that all the scriptures spoke of Christ on the road to Emaus.
2. They returned to Jerusalem and told the disciples.
3. The disciples wished to reproduce the sermon on the road.
4. They studied the scriptures (OT) for that purpose.
5. They were given the Holy Spirit to remind them of what they were taught, and lead them in truth.
6. As they studied the OT, the Spirit correlated scripture with what Jesus did and said.
7. They taught what they learned in the Jewish church, not the Gentile church.
8. From time to time, they collected the teaching in the Jewish church, and threw it over the wall at the Greek church, which did not wish to learn Hebrew.
9. Mark was the first record, which was updated by Matthew and Luke. (and John)
10. Each revision added new things they discovered, and removed things that, though true, caused teaching problems in the church that was being Hellenized and has even less interest in Hebrew scriptures.
11. The differences between them can be reverse engineered to confirm the first century hermeneutic.