Answer
Distance from Hamilton to Fort Lauderdale $\approx 1027.96551724$
Distance from San Juan to Hamilton $\approx 964.844827586 $
Work Step by Step
Since the measured distance from Fort Lauderdale to San Juan is 58 mm, and the actual distance is 1046 miles, for the sake of approximation we may assume that the actual distance is the measured distance multiplied by some scaling factor, call it $a$.
Thus, we have the following equation:
$a * 58 = 1046 \implies a = \frac{1046}{58} \approx 18.0345$ (dividing by 58 on both sides)
Now, in order to find the distances from Hamilton to Fort Lauderdale and San Juan to Hamilton, we can multiply by the same scale factor $a$ respectively:
$\implies \frac{1046}{58}\cdot\left(57\right) \approx 1027.96551724$
and
$\implies \frac{1046}{58}\cdot\left(53.5\right) \approx 964.844827586$
