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We extend the upper bounds derived for the horizontal and radial chemicaldistance for 2d Bernoulli percolation in [DHS21, SR20] to the planar randomcluster model with cluster weight $1 \le q \le 4$. Along the way, we provide acomplete proof of the strong arm separation lemma for the random cluster model.

Nontrivial upper bound for chemical distance on the planar random cluster model