If the U.S. wants to take back the lead in the recently reignited space race, it would do well to remember the old adage from little league: teamwork makes the dream work.

At present, some of the top minds in the world are working toward colonizing Mars and taking earthly talents into the great beyond. Unlike the great space race of the 1960s, this one is predominantly led by the private sector.

Boeing Co. (BA) - Get Report and SpaceX, the space exploration brainchild of Tesla Inc. (TSLA) - Get Report CEO Elon Musk, have broken away from a pack that also includes Amazon (AMZN) - Get Report founder Jeff Bezos' Blue Origin. This week, Boeing CEO Dennis Muilenberg told TheStreet's Executive Editor Brian Sozzi that his company will undeniably beat SpaceX as the first company to get to Mars.

"I firmly believe that the first person to step foot on Mars will get there on a Boeing rocket," Muilenburg said. He added that Boeing is working with NASA to build a rocket space launch system, with initial construction already in the works.

SpaceX chief Musk then took to Twitter to up the ante.

But instead of just focusing on their singular missions, U.S. based manufacturers Boeing and SpaceX should join forces. For example, what about pooling resources to more quickly fire off jointly manufactured rockets that take aim at Mars? Or, how about Boeing takes a stake in SpaceX to support their ambitions and provide financial support (while also partaking in the upside)?

SpaceX could benefit from both Boeing's strong balance sheet and its positive relationship with the U.S. government. The 102-year old Boeing could tap into the entrepreneurial spirit of Musk and his team at SpaceX.

"I tend to think it will be a hybrid," said Chris Carberry, CEO of Explore Mars, on who will be the first aerospace company to help step foot on the red planet.

"It's a rivalry, it's competitive. But in some places we work together. We launch satellites today on SpaceX rockets," Muilenburg quipped. See? It's not that hard to work together.

"It's not as though Boeing is going to Mars on its own either," said Carberry. "Boeing is very much linked to the architecture that NASA is working on. SpaceX has been working on its own separate architecture, but it's unclear how they will pay for the innovation they have on tap."

To its credit, upstart SpaceX dispatched the first privately-funded liquid-fueled rocket to reach orbit. It was the first non-government entity to send a spacecraft to the International Space Station. It was also the first to land a first-stage orbital-capable rocket. And that's all happened in a short 16-year existence.

But imagine what would be possible if SpaceX had access to Boeing's gargantuan cash pile (Boeing estimates $15 billion in operating cash flow alone in 2018) and 102 years of engineering experience.

The two have the support of the government, too, at least under the Donald Trump administration. President Trump has previously said he wants Mars travel to become a reality "within [his] first or second term." While that might be a bit of a lofty goal, it does illustrate the Trump administration's commitment to space exploration.

As does the budget: the fiscal year 2019 budget (starts Oct. 1) calls for a roughly $370 million increase in spending for NASA.

"We're going to go back to the moon. The administration is really leaning forward on returning to the moon, setting up a lunar station and then using that as a stepping stone to Mars," Muilenburg said.

"The government is highly unlikely to give it all to SpaceX or any one company," Carberry said. "They have to find that right balance between innovation ... but also that tradition, that experience Boeing and [Lockheed Martin Corp. (LMT) - Get Report ] have."

If the White House is opening the floodgates for space exploration to private enterprises in addition to the likes of NASA, it's clearly trying to set a precedent for collaboration. Muilenburg and Musk should take a page from Washington's book and put their heads together. If we want to live on Mars someday, that might just be the only way to turn a dream into a reality.

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