In chapter 20, the Duke makes a handbill advertising Jim as a runaway slave, and concocts a story that they are too poor for a steamboat or chains.
The Duke decided that it would not be safe for them to travel with Jim, because anyone who saw him would think they were helping him run. He says:
“Whenever we see anybody coming we can tie Jim hand and foot with a rope, and lay him in the wigwam and show this handbill and say we captured him up the river, and were too poor to travel on a steamboat, so we got this little raft on credit from our friends and are going down to get the reward” (enotes etext p.90)
He notes that chains would have a better effect, but to match their story they should use ropes. They will only tie Jim up with the ropes when they seem someone coming. Like Tom Sawyer, the Duke is more concerned with creating a dramatic story than with practicality.