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The phrase "at a speed" is correct and usable in written English.
Depending on context, it can be used to indicate the rate of an action or process. For example, "I finished the job at a speed that surprised even me."
Exact(59)
Poverty would be reduced at a speed previously unimaginable.
Intel's top Pentium runs at a speed of 1 gigahertz.
The bus was "creeping along", witnesses said, at a speed not registered on the speedometer.
The evidence has to be gone through laboriously at a speed that lay people can understand.
They traveled at a speed of about three kilometers a day.
He still writes a great deal, at a speed at which most people read.
Tests were developed at a speed of 1 mm/min.
To travel through beautiful scenery at a speed of four horsepower is just marvelous".
Carrying 12000 pound, it moved at a speed of.
It had a range of 20000 m at a speed of 48 kn, 32000 m at 40 kn, or 40000 m at a speed of 36 kn.
The missile, traveling at a speed of 1,900 mph, decimated the airliner.
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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