If any licensed electrician told you anything other than using two separate
circuits, stay away from him. Fishing a new wire next to an existing wire in
a conduit is sometimes a pain. Depending on the size of the conduit, it
might be easier (and faster) to use the existing #6 wire to pull 2
completely new sets of wire.

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oups.com...

My suggestion: leave the existing 60 amp wire and box, change its
breaker to 40 amps, and use it for the 40 amp load. For the other
load, run a separate, new, 30 amp line with a new box.

Cheers, Wayne

Thanks Wayne. That's what I'm going to ask my electrician to do. I hope
fishing the #10/3 thru the steel conduit with #6 wires in there won't
be a problem. The good news is, the breaker box is also in the kitchen.

As far as some of the other replies go, I have no intention of going
against the code, but as I said in my first post, I got conflicting
answers from licensed electricians, and just wanted to clarify things.