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The only ratios I see listed for a Ford 9" in that range is 3.25, 3.50 and 3.70. Sounds like the rear might have been replaced at sometime in the past.
Post what the warranty plate on the driver's door has for the axle code and I'll see what came in your truck from the factory.
Hi- IMO, the F100 model is too much of a lightweight for what you want to tow. The F100 is basically a car chassis/suspension and to tow an 18' car hauler with a car on it would exceed it's capability. I've been around campers, motorhomes, trailers my entire life and you would be disappointed with the performance of the truck. Plus the components, like brakes, cooling system, electrical, springs, etc. are not designed for towing that much nor for hauling much. Even with electric trailer brakes, your setup would not be safe for handling and stopping. An F250 is what you need. Good luck!
I used to do this all the time with my F100. Don't!
I wobbled around, I slid went trying to stop. When I didn't slide the brakes just wouldn't stop. It felt very uneasy and I went very slow. When I started towing with the 1979 F250 Crewcab it was completely different, stopped good, didn't wobble around, didn't spin with trying to take of easy.
I did not tow when the road was wet either.
You have been warned! lol