A California company has communicated with the Michigan Department of Transportation about a futuristic transportation system that could approach the speed of sound to and from Detroit.

A spokesman for the state agency said Hyperloop Transportation Technologies Inc., based in Los Angeles, has "made contact and while there is no meeting scheduled, we are always willing to listen." He did not respond to follow-up questions.

The company, which is seeking to build a national network of high-speed commuter trains that could travel at speeds up to 760 mph, said last week it has signed "official agreements" with the Illinois transportation department and North Ohio Areawide Coordinating Committee to start conducting a feasibility study on building a system that would provide 28-minute commutes to Cleveland from Chicago.

"We see outstanding potential and economic benefit in connecting Detroit to our Great Lakes Hyperloop network," Robert Miller, chief marketing officer for the company, said in an email to Crain's. "At this time however we cannot comment on ongoing conversations."

Perhaps the best known hyperloop advocate is Tesla and SpaceX CEO Elon Musk, who proposed such a system to connect Los Angeles and San Francisco for what he estimated was $6 billion to $7.5 billion. Hyperloop Transportation Technologies later proposed a similar concept that would cost $7 billion to $19 billion.

But how much would, say, a route from downtown Detroit to downtown Chicago cost, based on HTT's estimates of $20 million to $45 million per mile? A lot. There's about 300 miles between the two, so based on those numbers you're looking at $6 billion to $13.5 billion.