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The phrase "are rapidly approaching" is correct and usable in written English.
It can be used to indicate that something is getting closer in time or distance, often in a context of an event or deadline.
Example: "The deadline for submissions are rapidly approaching, so please ensure your work is completed on time."
Alternatives: "are quickly nearing" or "are fast approaching".
Exact(60)
Deadlines in the remaining states are rapidly approaching.
Today's players are rapidly approaching long-existing records for a variety of reasons.
"We are rapidly approaching a common language," says Gregory Berns, a neuroscientist at Emory University.
Does the Earth have some sort of carrying capacity that we are rapidly approaching (or have already exceeded)?
It is becoming clear that we are rapidly approaching the point at which further waiting would be futile.
President Trump and his chief trade negotiator, Robert Lighthizer, have set a series of crucial deadlines that are rapidly approaching.
The switches are rapidly approaching dimensions that can be measured in terms of the widths of just a few atoms.
"But I expect that to end, now that the Republicans have started this stunning slaughtering of each other" and the primaries are rapidly approaching.
At the Washington Free Beacon, Matthew Continetti wrote, We are rapidly approaching the moment at which Washington reevaluates the Obama campaign's reputation for competence and expertise.
The US and UK markets are rapidly approaching saturation point: about 70% of all mobile phone owners in both countries have a smartphone.
With the reduction in assets arising from the falling endowment and significant increases in new debt incurred during the 1990s, we are rapidly approaching that limit.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com