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I have seen a few people use synthetic oil and swear it has to be the reason their engine is still running at 200k plus. I can count more cars that are still running fine at 250k and up on conventional motor oil. Truth is modern engines are built well and other things are more likely to wear out before internal engine parts. That being said you are supposed to get more miles between oil changes with synthetic. And some claim to gain fuel economy (I don't know how often they actually gain and how often they brainwash themselves...). The downside is cost. There is nothing wrong with synthetic, it's good stuff. Don't confuse good with a gift from god as some claim. I've seen the real world difference and it didn't brainwash me.
The transmission on the other hand will be tough to get to the 300k mark if you tow. I'll leave the question open for others to chime in on maintenance tips/intervals for extreme use.
Yes, you will get better durability with synthetic but the question is "how much more" and will the extra cost of oil through all those years be worth it.
Now the transmission question: The transmission needs 2 things to last forever. It needs fresh clean oil at all times and it needs to be kept cool. Do a complete flush (without chemicals) every 30K and install the biggest trans cooler you can find and that trans will go forever. You don't need any synthetic oil, just clean oil, and don't overheat it.
It is not a value to the point you'll be told if you ask 100 auto techs. It's expensive insurance with no guarantee. It's gambling.
250 was a rough number. But their driving habits and maintenance habits vary. What is more important than changing the oil is keeping clean oil in the engine. One trip around the block with coolant mixed in the oil is more harmful than driving 25k on the same dino oil. One short road trip after an engine has been flooded (to the point gas mixes with the oil) is more harmful than... A properly tuned clean burning engine is the key to longevity.
There is opportunity cost with synthetic. What if the car is wrecked? What if you change your mind and trade it in (do you think the dealer is going to give you extra on trade at 150k cause you used synthetic, he might lead you to believe he is...), etc
All this said, I'm not an opponent of syn oil. But I think the fans of syn are blowing the horn to hard.
If you do switch stop back and let us know if there is a difference in gas mileage. If there is an actual difference in mpg it's probably worth it.
Another thing to consider, you vehicle may have an internal engine or trans design flaw that will keep you from reaching 300k troublefree. I haven't found a dealer tech (you pick the nameplate) that praises new car quality.
I'm a firm believer in changing fluids at Regular intervals. When fluids are left in a car too long they become contaminated with dirt and moisture. these contaminates cause chemical reactions some of whitch form acids in the fluid.
Like moisture in used engine oil it forms pudding and It's known fact that acid although mild form in the oil.
A transmission flush is something you can't do yourself. There is a machine that does a complete fluid replacement, including what's in the torque converter and not just what's in the pan. It usually costs less than $100 including the fluid. Just tell them not to use any additives when they do it. They aren't necessary.
PS, as far as the manufacturers are concerned, there are no extended intervals for using synthetic oil. They require the same intervals. I personally wouldn't advise going over 7 or 8K with synthetic. I use it on my personal vehicle at 10K intervals but I change the filter and add a quart every 3K. Manufacturers won't support that though.