As a train nears the Great Salt Lake in Utah, a Mormon man gets on board, dressed as if he were a member of the clergy. He is a Mormon missionary named Elder William Hitch, and will be giving a lecture in car no. 117 on Mormonism. Passepartout is intrigued, and decides to go listen.
He talks about how the government has been trying to oppress Mormons under its rule, but how they have been resisting and redoubling their efforts. He tells the history of the Mormons from Biblical times to the present. Some of the listeners wander off, uninterested in what he is saying, but Passepartout stays. Eventually only Passepartout is left listening, and the Elder is speaking directly to him. When the elder asks him if he will "plant his tent" (pg. 108) under the shadow of the Mormon flag, Passepartout refuses, and leaves the car at last.
The train makes a stop at Salt Lake City and Mr. Fogg and his group have some time to visit it. It is a very American town, built as a checkerboard like most others. As they wander and pass by Mormon women, Passepartout wonders at the phenomenon of polygamy that is practiced by the Mormons. He decides he pities the husband, who is tasked with guiding so many wives through life.
The train enters mountainous, dangerous terrain. As usual, Mr. Fogg is calm, cool, and collected, but Passepartout is worried by the possibility of delays. At one point, Aouda recognizes Colonel Stamp Proctor, the man who fought with Mr. Fogg back in San Francisco, on the train. She is alarmed because she has grown attached to Mr. Fogg in a way that she acknowledges is more than just gratitude. She tells Passepartout and Fix when Fogg is asleep, and they are all worried about Fogg realizing that Proctor is here and getting into a fight with him. To distract Fogg, they acquire a deck of cards and engage him in a game of whist.
The train continues on through the American wilderness, but eventually makes an unscheduled stop: the bridge that they need to cross is in bad condition, and will not hold their weight. They have sent a telegraph to call another train, but it will likely be six hours before it arrives. Everyone is upset, but a man named Forster suggests that if they approach the bridge at extremely high speed they have a good chance of getting over.
Passepartout is not sure about this, and thinks the proposal is a little too American. He has a simpler suggestion to allow the people in the train to cross on foot first and then let the train come after, but no one allows him to speak, even though he tries over and over again to get a word in. Finally, they give it a shot. At a hundred miles an hour, the train makes it over, just before the bridge comes crashing down into the river rapids.
Halfway through the train trip, much to Aouda's dismay, Fogg and Proctor encounter each other. Each still angry about what happened in San Francisco, they agree to engage in a duel. They try to do it at the next train stop, but since the train is late it just continues on without stopping—instead, they do it on the train itself. They clear out a car in the rear of the train, and Proctor and Fogg each have a revolver.
As they are about to begin firing, though, the train is suddenly attacked by a band of Sioux Indians. They swarm the train and the passengers bravely try to fight them off; even Aouda defends herself with a revolver. They need to figure out how to stop the train, because unless the train stops at the next station (a fort with soldiers), the Sioux will win the conflict. Passepartout figures out how, but just after that, he and a number of other passengers go missing, presumably kidnapped by the Sioux.
As they tend to their wounded at the fort, Fogg is determined to find Passepartout, living or dead. He understands that even a single day would make him miss his ship in New York, but he knows that it is his duty to find his loyal servant. He decides to go off in pursuit of the Sioux, and the captain of the fort sends thirty soldiers to go with him. He asks Fix to remain with Aouda and keep her safe. Fix agrees, and then wonders why he did—he cannot figure out why he is so fascinated by Fogg, when his goal is to arrest him.
The train prepares to leave once more, with Fogg still gone. Aouda refuses to go, and even though Fix originally thought he would, he realizes that something is holding him back. They remain at the fort, and wait a long time for Fogg and the others to return. At last he does, having rescued Passepartout and the other captured travelers.
They are now twenty hours behind schedule, and Passepartout once again berates himself for being the cause of the delay. Fix, however, proposes that they make up the time by riding on a sledge (sled) to catch up with the train in Omaha, Nebraska. Since it is winter, there is snow on the ground, and the sledge has sails to catch the wind, it can move even faster than an express train. Led by the sledge driver, Mudge, they make it to Omaha through the cold, just in time to catch a train. The rest of the train trip to New York progresses without incident—however, once they reach the harbor, they realize the steamer had left merely 45 minutes before.
In his exploration of different belief systems, Verne often paints caricatures of certain religions. This was initially seen during the group's journey across India, when Hinduism was portrayed as exotic and often barbarous, and it comes into play again in these chapters with Mormonism. Verne clearly thinks Mormonism is a strange product of the religious freedom on which America prides itself. He takes hold of many of its stereotypes, particularly polygamy, and Passepartout's comic thoughts on the subject give insight into Verne's own thoughts about it.
Notable is that Passepartout comments that in a polygamous situation he feels bad for the men, since they are responsible for looking after so many women. This also fits with the previously discussed misogynistic views of this time period, that suggest that women do not have their own agency and are not as worthy as men.
In these chapters, an unlikely alliance forms between Aouda, Passepartout, and Fix. All three are attempting to protect Mr. Fogg as best they can and help him get back to London, but each has very different motives. Aouda is motivated by her blossoming love for the man who saved her back in India. Passepartout is motivated by deep loyalty to his master and his cause. Fix, on the other hand, is motivated by his sense of duty: he needs to get Fogg back to England safely so that he can finally do his job and arrest him. There is some dramatic irony here, in that Fogg has no clue that these efforts to keep him safe are occurring—he is far too preoccupied with emerging triumphant in his wager.
Passepartout's lack of power is once again highlighted during the train trip across America. When they attempt to cross the bridge, Passepartout serves as a voice of logic and reason in a heated moment of panic, proving that he is actually cleverer than he is given credit for. However, because he is merely a servant, he has no power or influence and is merely silenced. Luckily no one is hurt and they make it across, but this example further proves that Passepartout is under-appreciated for his talents.
Passepartout's role in this entire journey is one of contrasts. He frequently and unintentionally delays their trip with the misadventures in which he manages to find himself, but on the other hand, he has saved them all on more than one occasion, starting with saving Aouda back in India and now managing to stop the train at the fort. As a good foil should, he also brings out the best in Mr. Fogg, who truly has come to care for his loyal servant.
Fogg is undergoing the transformation expected of a protagonist on a journey. As time goes on, his tough and stoic outer exterior begins to give way as he shows true affection for both Passepartout and Aouda. He was willing to lose his wager to rescue Passepartout from the Sioux, and he consistently shows gentlemanly cordiality and care to Aouda, wanting to keep her safe and protected. Fogg's softer side is certainly emerging as they near the end of the trip.
Just like with the tribes living in India, Verne depicts the American Indians that attack the train as savage, wild, and almost less-than-humans. He describes them descending in swarms and being picked off like a herd of animals by the courageous train passengers. In this scene, the contrast between late 19th century visions of "civilized" and "uncivilized" peoples is presented, a troubling theme that permeates this entire novel.
As they slowly draw nearer to Europe and the eighty-day mark of their adventure, the challenges that Fogg and his group face grow bigger and more absurd. This trend of growing obstacles suggests that in the final leg of the trip from New York to England, they will have to think up the most ridiculous solution yet to get them back in time for the wager. Chapter 31 ends with a cliffhanger, as they arrive in New York to find the ship already gone. But Fogg has not given up yet, and certainly will not give up in the home stretch.