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"until they reached" is correct and usable in written English.
You can use it when expressing the duration of an action that continues up to a certain point in time, and ends at that point in time. For example: The hikers trekked up the mountain until they reached the summit.
Exact(60)
Until they reached for an Asbo.
Some remained enrolled until they reached 21.
They walked in silence until they reached the lake.
"They simply kept going until they reached agreement," he says.
All cases were run until they reached a steady state.
The oBM-MSCs were isolated from the iliac crest and cultured until they reached near-confluence.
Cell viability was maintained by providing a fresh medium every other day until they reached confluence.
Each species was prepared as described above and grown until they reached the log phase.
More specifically, the dry samples were heated in a laboratory kiln until they reached 950 °C.
They continued to change the composition of the cards until they reached the correct card composition.
The steel fibers at the crack surface continuously resisted until they reached their bond strengths.
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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