Rome and China

An interesting question to wonder is what would happen if Rome and China actually met. The small things that they heard of each other didn't seem to interest either of them. Though if they were to meet, what would the results be? Would they work together and gain economically? If so, would this save Rome from destruction or only prolong it? Would the two empires, warlike by nature, go at each other in order to be dominate like Rome did to Carthage and China did to Vietnam? There are so many questions that come up that cannot be answered. Any reaction would deeply affect the future of both empires greatly.