Answer
from San Juan to Hamilton $964.84\ miles$,
from Hamilton to Fort Lauderdale $1027.97\ miles$.
Work Step by Step
Using proportions, we have $\frac{d_{SH}}{53.5}=\frac{d_{HF}}{57}=\frac{1046}{58}$, thus the actual distance from San Juan to Hamilton is $d_{SH}=\frac{1046}{58}(53.5)\approx964.84\ miles$,
and from Hamilton to Fort Lauderdale $d_{HF}=\frac{1046}{58}(57)\approx1027.97\ miles$.