(Semantically, “ten minutes' walk” still means ‘a ten-minute walk’ rather than ‘the ten-minute walk’, but your point in reply to shminux was about syntax not semantics anyway.)
The "proof of synonymy" looks like this:
ten minutes' walk = (the walk) of (ten minutes) = a (walk of ten minutes) = a ten-minute walk
...the second "equality" being where semantics is invoked.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Of course, for "every Monday", the last one should have been dated July 22-28. *cough*