The "Competitive Eaters and Friends" team became the fourth team eliminated from the around-the-world competition after arriving at the fifth leg's Pit Stop at Hotel Benvengudo in Les Baux, France in last place.
"It's sad. We really love racing this, but I'm happy me and Tim competed. I'm happy he's my partner," Joey said following his team's ouster. "There were things I couldn't have done that Tim did during the Race, and we succeeded together and we fell together."
Tim added, "It was a tremendous privilege to get to do this, but I think we left so much undone that I don't know when I can let go of the feeling of missing out because of our own failures."
The teams' first set of clues instructed them to drive 120 miles inland from Saint-Tropez to Les Baux, which is famous for its ruins, sleepy villages and lovely landscapes. The clue would be waiting for them in a castle city called Chateau des Baux.
Lucas admitted to the cameras he was waiting for the perfect time to pop the question and he would know when the moment is right.
Alex and Conor arrived at the Chateau des Baux in first place. They were soon followed by Kristi and Jen, and then the other teams trickled in one by one.
Everyone discovered that the Chateau des Baux was closed until 8:30AM, so it was time to rest, sleep on rocks or just waste the clock.
Once the doors opened, the teams viewed giant weapons that were used for launching 200-pound boulders at invaders.
Alex and Conor ripped open the clue in first place, and then they were followed by Lucas and Brittany, Kristi and Jen, Henry and Evan, Eric and Daniel, Jessica and Cody, Trevor and Chris, and Joey and Tim.
For this Roadblock task, one member from each team had to use the materials provided to make this iconic catapult weapon and then transport it to a soldier.
Eric opted to try the Roadblock, and he was joined by Henry, Cody, Tim, Lucas, Kristi, Chris, and Conor.
Kristi was clever in her use of material and attention to detail, while Lucas also proved himself to be a pro at building things. And since Cody hopes to build houses after The Amazing Race, Jessica hoped her boyfriend would get the job done quickly.
Lucas and Cody did not get their catapults approved on their first attempt, but in the end, Lucas and Brittany still completed the Roadblock task in first place.
Cody and Jessica accomplished the task in second place, and on their heels were Kristi and Jen, Eric and Daniel, Henry and Evan, Trevor and Chris, Tim and Joey, and finally Alex and Conor, who had a tough time with the task.
The teams' next set of clues told them to proceed to Cafe De La Fontaine and ask a man enjoying a glass of red wine for their next clue.
Lucas and Brittany kept their lead and grabbed the clue in first place. Behind them were Kristi and Jen, Jessica and Cody, Eric and Daniel, Henry and Evan, Trevor and Chris, Alex and Conor, and finally Joey and Tim.
It then became time for the teams to select one of two possible Detour tasks: "Full of Bull" or "Colorful."
"Full of Bull" required the teams to search among hundreds of bull replicas in a giant arena for red, white and blue ribbons.
"Colorful" required the teams to unlock a piece of 3-D artwork featuring a bridge in order to receive their next clue.
Because the painting task appeared to be some type of puzzle, most teams didn't even want to attempt it.
The teams reasoned that it's better to do a task with an obvious start and end point, even if it's more physically taxing. A puzzle, in other words, could potentially take hours to complete.
On the way to their Detour, Cody and Jessica got a little lost, and Jessica blamed the mistake on Cody because he often makes decisions based on his gut instincts or his "hunches."
Cody has confessed on numerous occasions he needs to listen to Jessica more often, but when it becomes time to follow through on that, he struggles. But Jessica didn't seem any less in love with her man, and she was barely even frustrated.
Alex and Conor also got lost at this point in the leg. As for Joey and Tim, they spotted the location of the bull task while driving around.
However, the guys agreed they didn't want to do a Detour task that required a lot of running, so they kept driving to find the painting task. It appeared, however, they also got lost, as did Trevor and Chris.
The only team who chose to do the "Colorful" task was Joey and Tim, and the guys had trouble figuring out how to unlock the painting.
Lucas and Brittany completed the Detour task in first place. They were then followed by Kristi and Jen, Eric and Daniel, Henry and Evan, Alex and Conor, Cody and Jessica, Trevor and Chris, and finally Joey and Tim.
The teams then learned they must proceed to the Pit Stop at Hotel Benvengudo.
Lucas and Brittany stepped on the Pit Stop mat in first place, and that's when Lucas proposed! The pair won a trip for two to Bali, and then Lucas asked his longtime girlfriend to marry him, and her answer was, "Of course!"
Brittany cried tears of joy, and the couple celebrated with other teams as they trickled into the Pit Stop one by one.
Kristi and Jen finished in second place and got to witness the entire proposal, while Eric and Daniel arrived at the Pit Stop in third place and caught the tail end of it.
Henry and Evan finished the leg in fourth place, Alex and Conor claimed fifth, Cody and Jessica ran up to The Amazing Racehost Phil Keoghan in sixth place, and then Trevor and Chris escaped elimination by arriving in seventh place.
Once Joey and Tim arrived, they learned their unfortunate fate in the Race.