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I have an alternate solution

Bend one of the fuses so the two ends are touching at the center point of itself, then light the center of that fuse, and one end of the other fuse. When the bent fuse has burned completely, you have 3 quarters of an hour remaining on the other fuse.

This works because lighting the center of the fuse is like cutting it in half, doubling it's burning time, just like lighting both ends at once. If both ends are lit, in addition to the center, the total burning time is reduced to one quarter of it's original time.

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