Three begin a meal together and two of them finish before the third, they can begin the zimun forcing the third person to interrupt his meal and respond. Since they are the majority they do not have to wait for him. (ShA1 – MB1,2)
Even if the two are not in a hurry it is at least a midda of Derech Eretz for the third person to interrupt his meal and answer so the others can go. (BeH “she’ochlu”)
What if the third person doesn’t want to stop eating and he will not answer? The two can still do the zimun as long as the third one is present – they will be yotzay and he will not be yotzay. (ShA1 – MB3)
If one of the three finish the meal before the other two, he cannot force the other two to interrupt and answer the zimun. However, they should go beyond the letter of the law for the individual who wants to leave. If not, the one must wait for them. He may not bentch without a zimun. (ShA1 – ShaH7)
If the one needs to begin bentching urgently (e.g. money loss is at stake) and the others still do not wish to interrupt, he can be maykil and bentch without a zimun relying upon the poskim who hold that the obligation for zimun does not begin until they all finish eating. The remaining two will need to look for a third person from outside to join them for zimun. (MB5 – ShaH7)
When the one who finished first waits for the other two to finish, they may not delay him further once they are done eating. (BeH “odd”)
The interruption should be until after “…hazon ess hakol…” Then resume eating the bread. When you come to bentch, begin from the beginning. (Rama2) LAWS OF BIRKAS HAMAZON