"So they rose up that very hour and returned to Jerusalem, and found the eleven and those who were with them gathered together" (Luke 24:33). Although the day was almost gone, their news was too precious to keep to themselves overnight. They excitedly traveled back to Jerusalem. They would not rest until the apostles knew of what they had witnessed! It is still true today that one who thoroughly understands and genuinely believes a spiritual truth will feel compelled to share it with others. There will be an urgency to do such!
"The Lord is risen indeed, and has appeared to Simon!" (Luke 24:34). This is what the two disciples were told by the others before they could speak. Clearly, Jesus' resurrection was not a hallucination or made-up story of the women (as they now knew personally and as others were learning!). When did Jesus appear to Simon Peter? It is possible that Peter went back to the tomb later that day (after hearing further testimony from the women) and saw Jesus in the burial garden. Or, it could be that Jesus simply appeared to him when he was alone sometime that Sunday. Since no details are recorded, it is impossible to know. Additionally, it is impossible to determine chronologically if Jesus appeared first to the two disciples on the road to Emmaus or to Peter. This is the case since it would have taken a couple hours for the men to return to Jerusalem, and Jesus could have appeared to Peter during that span of time.
"And they told about the things that had happened on the road, and how He was known to them in the breaking of bread" (Luke 24:35). The meaning is that Jesus' identity was revealed to them when He broke the bread. It could be that the manner in which He broke the bread identified Himself, although such is not demanded by the text.
"They did not believe them either" (Mark 16:13). The apostles in general did not believe the women or these two disciples (perhaps because of some of the details of the alleged appearances). However, it appears that at least some of the apostles believed Peter (cf. Luke 24:34), though the hearts of others were skeptical and still full of doubt.