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A 20% slope is only an 11.3 degree angle. A PT425 with a bucket full of stone could go up that without issue. Pulling a trailer is a different story.
The reasons are these:
Going up hill, there's more weight on the rear tires. If you put a load of stone in the bucket and lift it off the ground even just an inch, that will transfer a lot of weight to the front tires, you'll get a lot better traction, and up the hill you'll go.
If you put a trailer on the rear vs a load of stone in the bucket, that would concentrate more weight on the rear of the machine and you'll lose even more traction on the front.
I've posted a few videos of my brush cutter going up hill, so maybe that's what you saw. A couple things to note if that's the case:
My PT425 is a 2001 model. The newer models have larger wheel motors so they are stronger on hills than my 19 year old machine.
When I'm pushing the brush cutter in float up a steeper grade, with the brush cutter in float, the brush cutter's weight is riding on it's own wheels and the PT425 is just pushing it. Eventually I'll start to loose traction on my machine in all 4 tires as the slope gets steeper. If I pull back on the joystick, taking it out of float, that take's the brush cutter off of it's own wheels and transfers its weight to the FEL arms on the PT425, effectively transferring the entire weight of the brush cutter and part of the FEL arms from the brush cutter to the PT425's front tires. It also takes some weight off the rear tires. What that does is concentrate several hundred pounds of force to the front tires for better traction. Then up the hill I go. Works quite well.