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The phrase "a different rate" is correct and usable in written English.
It can be used when discussing variations in speed, frequency, or cost in comparison to something else.
Example: "The service is offered at a different rate for premium members compared to standard members."
Alternatives: "an alternative rate" or "a varied rate".
Exact(60)
Their brains fire at a different rate.
Each one of them prints at a different rate.
"You could in the future have a different rate of income tax," the prime minister said.
The cement expands at a different rate than the sand and gravel, causing cracks.
They will be doing it at a different rate to today.
There are four types, all paying a different rate, and it's necessary to authorise each one.
Each fertilizer is applied at a different rate, measured in pounds or tons per acre.
Could antimatter fall upward – that is, exhibit anti-gravity – or fall downward at a different rate?
This makes the lattice vibrate at a different rate and changes the critical temperature accordingly.
As the Yankees score runs at a whopping pace, Jeter is grading himself at a different rate.
The pen leapt again on the paper – blip, blip, blip – a different rate, but clearly the same kind.
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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