Racing around the world for the $1 million prize is hard work, and the eighth leg of “The Amazing Race: Unfinished Business” was evidence of that.

“You’ve been racing so hard, your cowboy hat is dirty,” Phil Keoghan, host of the CBS-TV reality series, said to Cord McCoy, who is racing with his brother, Jet, for the second straight spring season.  

“I’m going to win me enough money I’ll get me a new cowboy hat,” Cord told Keoghan after the team finished fifth in the episode that aired Sunday night. “It’s time to step it up, or we’re going to go home.”

The cowboys trailed the pack for much of the leg, which began in Varanasi, India. It marked the second straight episode the brothers finished in fifth place; they left the starting point at Ramnagar Fort an hour and a half behind the leaders, Globetrotters Herb Lang and Nate Lofton.

“We kind of dodged a bullet in the last leg, but I’m not sure we could do it again,” Jet said.

“The closer we get to the end, there’s room for fewer and fewer mistakes. I think the cowboys are about ready to get out of India. We’re done playing ‘Cowboys and Indians.’ ”

The first step in the eighth leg was to book a flight to Vienna, Austria, through a travel agent. While the other five teams took the earliest arrival, it involved two connections.

The McCoys opted for a travel plan that arrived in Vienna half an hour behind the other teams but involved just one connection.

“Every flight we’ve been on in this country has been delayed by 20 to 35 minutes,” Jet said. “I don’t know if it’s worth the risk. You can lose 30 minutes anywhere. I think we’re going to roll the dice.”

As expected, the rodeo cowboys were well behind the field. Once in Vienna, they made their way to a 2012 Ford Focus. As they backed the vehicle, they read through the car’s camera their next clue, taking them to Schloss Schallaburg, a castle that is widely known for its annually changing, cultural-historical and archaeological exhibitions. From there they were directed to the national library.

“Jet and I have been making a habit of starting in last,” Cord said. “You can’t survive and win a million dollars.”

Obviously they have through two-thirds of the race. At the library, the teams were directed to their “detour,” where they either carried a couch from Sigmund Freud’s home/museum to the university or tried to eat a large meal while riding 12 minutes on a giant Farris wheel.

Three teams – best friends Zev Glassenberg and Justin Kanew; sisters Jennifer and LaKisha Hoffman; and father-daughter Gary and Mallory Ervin – tried the meal and failed, so all eventually carried the couch.

“We just hope we make it to our location faster than a couple other teams,” Cord said. “When we were going to the couches, Jet and I knew we were dead last, so we had to pick up the pace.”

Just as the brothers reached the Freud museum, they saw Glassenberg and Kanew leaving with their couch.

“Hey, that was all we needed,” Cord said. “We’re back in the game. That was the first time Jet and I seen any team. That was like the first light at then end of the tunnel that we’d seen.”

“That’s kind of encouraging,” Jet said.

The brothers were shown running through the streets of Vienna, but they still had their senses of humor.

“I kept thinking it might be faster … I could lay on the couch, tell Cord about my feelings, and he could push me,” Jet said.

“I don’t need to know about his feelings that bad,” Cord said.

As they completed the task, they passed Glassenberg and Kanew, then they raced back to the library, where their vehicle was parked. At that point, the cowboys were ahead of two other teams.

“I think there’s two cars sitting there,” Jet said, as they prepared to drive to “Old Town” Salzburg. “There’s still hope for us.”

But the race was on, and Glassenberg and Kanew moved back into fourth place on the highway, passing the McCoys en route to the “road block,” where one team member had to dress the part and do the work of a chimney sweep, from dark outfit to the top hat.

“Looks good on me?” a joking Cord asked the actual chimney sweep assigned to help him. “Chicks dig it?

“I think I might have found a new calling already; chimney sweeping at its best.”

Once the task was complete, the teams found the clue to the leg’s “pit stop,” Villa Trapp, the home of the actual von Trapp family from the “Sound of Music.”

Glassenberg and Kanew won the leg, each earning a 2012 Ford Focus. The Ervins finished last, but they remain in the race because Sunday’s episode was a non-elimination leg. The father-daughter tandem will have to handle an extra task during the ninth leg of the race, which airs at 7 p.m. Central next Sunday.