Why did the transmission fail?
As quincy wrote, private vehicle sales are generally "as is" where you take the item at its face. That's why a private mechanic is worth the money to assess the vehicle. Also, any promises made in response to a specific question may have some warranty attached. Otherwise, promises can either be a factual representation or "puffery" depending on the context. The context and the promise would be very difficult to prove--especially since they were probably not mentioned in any writing you made to memorialize the sale.
That leave us with fraud and why the first question is important. Transmissions fail. A hard ride of three hours, depending on factors, could be very taxing on a transmission and could have it fail with no knowledge of weakness on the part of the seller. (That is not to argue you rode it hard and put it away wet, its just that three hours of actual driving introduce many factors that are not easy to assess.) The bottom line is that you are unable, absent a warranty of some sort to claim that because it failed soon after you got it, the failure is something that would have been known by the seller. That's why you have to look at why the transmission failed.
I don't know much about vehicles. I know the gas goes in the back in the hole I've added fuel to many times. I am informed and believe, oil goes in up front. Somewhere under the hood I believe. That being said, in the olden days I believe a person could put sawdust into a transmission to keep a failing transmission alive a bit longer. I don't know how it worked and I think it has not worked for decades; but, I'm sure there are other tricks that can be done today to trick a person into thinking there is not a problem with the transmission when there is. At least for a bit.
Take what you should consider as your vehicle to a mechanic. See what happened. If he has suspicions about what happened or if it has been recently "fixed", we might think further.