This is an easy one.
I stopped using Google Hangouts a while ago since messages I was receiving weren’t triggering any notifications, and I had to turn on the phone and manually check for new messages every few minutes. Even then it would take 30 seconds to retrieve messages sent 10 minutes ago.
When I first looked around for solutions I saw all sorts of accusations; it’s your task scheduler, it’s your Hangouts version, it’s your network.
My solution turned out to be much simpler. It turned out my wife was signed in to my Google account on her phone, and for whatever reason her phone was getting higher priority than mine– she would get messages (even those she sent) before I did, hence the delay.
So if you are having trouble getting Hangouts messages, check to see where your account is currently signed in!