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The phrase "at a rate" is correct and usable in written English.
You can use it to indicate something is happening at a certain speed or rate of progress. For example, "They are repairing the road at a rate of one mile per day."
Exact(60)
The characters are scrolling at a rate of 2.5 cps.
Compensation at a rate to be specified in each grant.
Data collection is conducted at a rate of 8Hz.
"The workload is going up at a rate of knots.
Medical aid gets funded at a rate of around 58%.
We're going at a rate of 2.5 a day.
We expect new technology at a rate like never before.
Waves come at a rate of 18 an hour.
Gardens change at a rate the human mind can understand.
At a rate of 26.8% you would pay back £569.55.
We're spending at a rate that's just unsustainable.
More suggestions(25)
at a rate parallel
at a rate considerably
at slight rate
at a rate unparaplleled since
bear interest at a rate
communications at a rate
deepening at a rate
difficulties at a rate
exactly at a rate
at a valuation
at a pacing
at a proportion
at a velocity
at a cost
at a prevalence
at a tempo
at a fee
at a mortality
at a rating
at a rapidity
at a tax
at a trend
at a growth
at a population
at a percent
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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