Emerson can dig 2 holes in 3 hours and johnna can dig 3 holes in 2 hours. six holes need to be dig. if emerson digs for 1 hour and then is joined by johnna, how long will they work together to finish digging the 6 holes ?

After 3 hours, Emerson will have worked 3 hours and dug 2 holes. Johnna will have worked 2 hours and dug 3 holes. So they'll need 1 more hole. Since Johnna works faster, we just need to add how much time she needs to dig 1 hole. It takes Johnna 120/3 = 40 minutes to dig 1 hole.
So they will finish digging after 3 hours and 40 minutes.