My kitchen sink backs up into my bathtub but the bathtub wont drain,drano or liquid plumber don't work?

plumbing is old and the little knob that lets the water drain is rusty and generally messed up,like i said the kitchen sink will drain but will drain into the tub and then the tub wont drain at all, and do it yourself plumbers have an idea,do i need a new tub.
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