I'm redoing the utility room in our 40 year old house, and I stupidly
removed the socket from the box to put in a GFCI without marking the
original wires. Stupidly because there has been some previous "work"
done by
possibly-incompetent folks, so I'm not sure what to make of this.
I've got
a blue wire and two white wires coming into the box, and the voltage
between
the two whites is 120, the voltage between one of the whites and the
blue is
120, and the voltage between the other of the whites and the blue is
240.
How is this possible? Or is there something obvious I'm missing? The
wires
themselves seem to be original wiring for the house, but I'm not sure
what
they might be connected to at the other end.

Any ideas what the blue wire was supposed to be originally for?

TIA!