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The phrase "a far slower rate" is correct and usable in written English.
It can be used to describe a speed or pace that is significantly less than another, often in a comparative context.
Example: "The new software processes data at a far slower rate than the previous version, leading to delays in project completion."
Alternatives: "a much slower pace" or "a significantly reduced speed".
Exact(11)
As yet this year, there have been only seven executions in Texas, a far slower rate than in 2000.
The camp has become overcrowded, with migrants still landing on nearby beaches – albeit at a far slower rate than last month.
The Scottish economy is growing at a far slower rate than the UK as a whole, with the North Sea oil slump leading to a fall in GDP last year, the latest data shows.
The mortality rate among premature babies has also fallen, but at a far slower rate.
In most major markets, physical retail continues to grow, albeit at a far slower rate than online shopping.
The rise continues afterward but at a far slower rate, until it approaches $9,000 a year around the time people turn 80.
Similar(49)
We have forecast a far slower growth rate of under 2%.There is clear evidence that passengers value savings to the time.
Over the past five years, the company has grown at a 66% annualized rate, but analysts who track cubist forecast a far slower 23% annualized growth rate for the next five years.
Buying and selling houses, though, is a far slower process.
So far this year, the economy has added an average of 194,000 new jobs a month, a slower rate than the 281,000 jobs created each month in the second half of 2014.
Sealed up in plastic garbage bags and buried under pound-upon-pound of plastic, glass, and paper, these scraps begin to break down at a rate far slower than you might think.
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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