This variation poses an additional restriction that burning is non-homogenous. That is, after 30 minutes, it need not be exactly at the middle of the string, burning.
The basic aha! moment for this puzzle is that if you start burning at both ends, then at the point where both flames meet and fizzle out, 30 minutes would have elapsed (assuming the string burns in one hour). One needs to take some time to grasp this point. After that, it can be generalized to super or sub lengths of the strings – if you burn the string at both ends, when the flames meet, half the time would have elapsed.
Thus, measuring 45 minutes with two strings is easy, then.