So it turns out the 3rd rocker from the front of the engine was just as loose. I tightened both and the ticking and carb backfire are now gone.
Wow. It would be awesome if it's just a matter of the nuts backing off. You may want to replace the ones that backed off with new ones. I hope the studs aren't pulling up.
At 175,000 miles, if nothing has been rebuilt like the heads, replaced camshaft, etc, the cam has to be worn out a bit, some lifters are probably shot as ed1948 mentioned, bent or worn out pushrods, worn valve springs, worn rocker arms, etc. If one part of your motor is suspect, like a valve or head issue, the engine will be out of sorts. Just like when spark plug wires are installed wrong, car bucks, runs rough, backfires, might not run at all. Get them sorted and it is like a different motor!
You mentioned you just got the car so who knows what history this motor has. How it was taken care of, especially as oil and filter changes go, might tell you where you need to go as far as repairing and refreshing this motor. Plus how you plan to use the car or what you want to do with it. How much gunk was inside the valve covers? If there was a good amount of sludge then few and far oil changes might be the norm here?
Getting the drive train right first should be priority # 1 in my opinion. This will maybe sound stupid, but if the car is not running it is mothing but a lawn ornament. You have so many options of rebuilding, dropping another motor in it, etc. whatever works for your budget and and how comfortable you are with your skills and experience in what you can do yourself and what you need help in doing.
I still have my original 305 in my 85. I have 109,000 miles on it and made sure to keep up with the maintenance since I bought the car new in late 84. I would love to drop a 400+ hp motor, but the 305 is running good and my situation of taking care of Dad restricts my budget spending which is fine. Life dictates so much of what we can and cannot do, and I would be ok if I never end up resto modding parts of the car and putting in a badder motor. I had the car new, drove it and enjoyed it for over 32 years and counting and do what I can within my means to keep it looking and running ok. So whatever you choose to do you will eventually have a car you can be proud of.
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