As they stand, only the first of your examples is correct. If, however, you remove "both" from the second example, both of the examples are correct, although they have, potentially, distinct meanings. The first example refers to the actual speed limits on the two roads; the second example (without "both") refers to the idea of a speed limit on both roads.
However, in practical terms, the distinction between the meanings (after "both" is removed from the second example) is likely to be a distinction without a real difference, unless at some point the context makes clear (a) that the speed limits on the two roads differ, and (b) that the difference between the speed limits on the two roads is somehow relevant.
Note that "both" can be also be removed from the first example without changing either its grammaticality or its meaning.