The physics
On a slope, the weight has two parts. Along the slope, it is mg sin θ. Across the slope, it is mg cos θ.
N = m g cos θ fmax = μ N
Static friction takes any value up to μN. It points whichever way stops the slipping. Once the block slides, friction is μN, against the sliding.
sliding down: a = g (sin θ − μ cos θ)
least hold: F = mg (sin θ − μ cos θ) least push up: F = mg (sin θ + μ cos θ)
From rest, a slide of length s takes t = √(2s / a). So a trip n times as long needs n² times less acceleration.
In a steady slide, μ = tan θ. Then the slope's total push equals the weight.