Cut through two perpendicular cylinders (intersecting faces)

I never have an issue intersecting different faces, but I am stuck. I have two cylinders that are the same diameter and are hollowed out. The intersect in a perpendicular fashion. The intent of the model is to make the tunnels, so I need to erase the crossing tube / cylinder. I cannot seem to get the faces to join so I can delete the crossing tube. Please help teach me the best way to accomplish this. Thanks in advance.

It looks like the horizontal cylinder is in a different context to the edges.
Make sure you have the intersecting geometry in the same context, either as raw geometry or within the same group/component.

Have a look at this. You can go through rather than just itersect the pipes.

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Click in sequence on the Scenes tabs of this SU file for ideas.

Intersecting cylinders.skp (496.4 KB)

The OP never came back.