I possess two wires

I possess two wires. Both of them have an inconstant thickness but both of them burns completely in sixty minutes. The problem is that I want to measure forty-five minutes while using these two wires.

How can I measure if cutting the wire in half is not possible due to non-homogeneous construction ?

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It is not as hard as it seems.
I will burn one wire on both ends and the other wire at one end only. The first wire will burn completely in thirty minutes and at that very moment, I will burn the other end of the second wire and it will burn in fifteen minutes.
Thus both of the wires will be burnt in 30 + 15 = 45 minutes