I am merging 2 websites and trying to decide which url to keep I have one domain that is 11 yrs old but it does not have any keyword relevance, and another domain that has keyword relevance that is 1 yr old? They both have roughy 4000 backlinks .
What do you suggest ?

I'd suggest you recreate the old one into a "branding" web site and use the new one as more of a search engine friendly web site with heavy cross linking between the two. In this way, should it be deployed effectively, you won't need to concern yourself with the accumalation of backlinks, ever again. Just keep evolving the two in their related but separate directions.

Could you please tell us why you want to merge these sites?

Well the company had 2 websites for some reason both with basically the same info, both websites was done with an online website program, and neither contain Seo, and even if they did I don't think it would be anywhere near as good as what could be accomplished with a real website. We have to have seo in order to make a profit their is no other way.

Furthermore one of the websites was built by a guy who is no longer with the company, and the company still receives the orders placed on the site, but they have no way to add new products or to get to the back office to make changes .

I am working directly with the owner of the company who is an older gentleman. He knows everything about what he does, and he is a very talented man. However he does not know the first thing about the internet, SEO, or operating a website.

Age of a domain matters. You can use your old domain and put them a keywords on metas as well as on your content.

Having keyword in the domain name are not helpful completely because many factors are also important in the success & visibility of any website in search engine. I prefer to continue with old aged domain.

The keywords are mostly useful in old crappy search engines. Keep the old one.

I think you should renovate your old website with new design and fresh content.

I would go with the Keyword rich domain, also it's one year old, if there is any debate like new domains are not received well by Google. One year old is, in my opinion, enough even if the age of a domain counts in SEO.

I think you should keep them both. One could be a blog and the other a website. Then optimize differently and see what happens.