Connecting bathroom to existing vent

[BMAC7]

Hello All,
I am new to this and have looked around the forum a bit. Everyone seems very helpful so I am hoping someone can give me some guidance on this issue.
I recently demo'd a half bath in a house I recently bought and found that the plumbing vent was terminated inside the wall. I know that I have to get it out of the roof and want to know if I can connect it to an existing 4" vent that was recently installed for the remainder of my plumbing fixtures. I've included a sketch of the condition. A couple questions:
- Is the 1.5" vent enough?
- Is the 20 horizontal run too much?
- Should I be concerned that I am connecting two cesspools with one vent? The eventual plan is to connect this plumbing to cesspool #.
Thanks for any help!

 

[Cacher_Chick]

As long as the horizontal section is pitched towards the drain it will function with no issue.

 

[Sponsor]

 

[hj]

When you say "cesspool", I hope you mean a septic tank AND cesspool, since a cesspool by it self would be an EPA violation and a ground water pollutant. As long as the vent can slope upward you can pretty much do whatever you want to with it.

 

[BMAC7]

Thank you for the responses, they are much appreciated.
I wasn't familiar with how to full system works, but yes, I did mean septic tank and cesspool.
Thanks again!