They left the house at 6 and would reach Edinburgh 12 hours later. (= .............. and they reached Edinburgh 12 hours later.)
This is from a famous grammar book. I don't understand how 'reached' and 'would reach' can have the same meaning.
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The Cambridge Grammar of the English Language (p198) states:
Would is also used to indicate futurity in the past, futurity relative to the time referred to by the preterite.
Left is the preterite in the sentence: They left the house at 6 and would reach Edinburgh 12 hours later.
The CGEL goes on to explain that with this use of would ...
... actualisation is entailed - and the actualisation is virtually required to have taken place, so that a simple preterite could have been used instead.
In other words, they did indeed reach Edinburgh 12 hours later.
A Comprehensive Grammar of the English Language (p216) has a similar explanation, noting that would in such contexts "can be understood to guarantee the fulfilment of the happening in question."
CGEL states that "This use of 'would' is restricted to narrative and similar genres", as in OP's example sentence.
They don't have the same meaning.
You would use would reach if you were writing about something that happened after they started their journey, but while they were still on their way to Edinburgh.
Reached would be used for something that happened after the journey was completed.