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Discover LudwigThe phrase "fast reaching" is correct and usable in written English.
It can be used when describing a situation or event that is quickly approaching or advancing towards a certain point in time or space. Example: The deadline for the project is fast reaching, and we need to work faster in order to complete it on time.
Exact(52)
Labs grow fast, reaching full size in about a year.
Of more immediate concern, the Saints' season is fast reaching the fail-safe point.
She served fast (reaching 119 miles an hour, averaging 109 m.p.h. on her first serve).
BTA-templated protein complex formation was also found to be surprisingly fast, reaching equilibrium within minutes.
Desmurget, M. & Grafton, S. Forward modeling allows feedback control for fast reaching movements.
MaB-flocs settled fast reaching up to a density of 19 g VSS L−1.
Similar(7)
By coach you're within easy, cheap and fast reach of the beaches on both the north and south coasts.
When the amount of ef-CNT exceeds 2.00 wt.%, vitrification stage of curing is fast reached, which lowers the degree of conversion.
That enables the Aqua Bounty fish to grow faster, reaching their market weight in about 18 months instead of 30.
Significantly, DSC exotherms were reduced and cyclization occurred much faster reaching a greater thermal stability when NIPAM was introduced at slow feed rates.
But the researchers also found that blue females sprint faster, reaching speeds of 1.5 meters per second compared with the 1.2 meters per second achieved by nonblue females.
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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