How do I fix the problem of water from kitchen sink backing up into the bath tub?

That is happening because you have a clog further down stream from both fixtures and the tub is lower than the sink. We need to rod out that drain. Are you above a basement or crawl, is there a clean out on the main? Back to you

The drain pipes are located under the house, I would have to crawl underneath the house. There isn't a clean out on the main. Please tell me how to go about rodding the drain? And what tools I'll need to accomplish it? Thank you very much for your help. This problem has been driving me crazy for weeks.

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Please tell me how to go about rodding the drain? And what tools I'll need to accomplish it?

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Bob nailed it! You have a clog downstream from the bath tub.
A hand held snake,(see image) is needed here for inside while to snake from the vent you will have rent a sewer machine,(see image)
You can reach clog from several places.
1) You may use the hand snake to snake from the tub waste and overflow, (see image) To snake your tub remove the two screws holding the chrome face plate and pull up and out on the linkage and plug. Feed your snake in through the opening. You will run into the return bend of the trap about 18 inches down but crank and work your way past that you should only have 6 or 8 more feet to run out. Flush with a tub of hot water.
2) Take a sewer machine up on the roof and snake the kitchen roof vent.
Run out enough snake to reach the base and 16 feet more. Good luck, Tom

You don't know how much I appreciate the help. I may go on this adventure this weekend. If not, when I do, I will let you know how it went. Thanks again.