Departure time of two ships crossing midway

Two ships leave islands $A$ and $B$ at the same moment, each sailing at a constant speed along the same route toward the other island. They pass each other at 1:00 PM. After that, one ship docks at 5:00 PM while the second does not arrive until 10:00 PM. When did both ships depart? Give the answer in 24-hour form without a leading zero (e.g. 4:30 PM is $1630$).

$700$ (7:00 AM). If both sailed for $t$ hours before meeting, then each ship's remaining distance equals what the other covered, which gives $t^2=4\cdot 9$ with the post-meeting times $4$ and $9$ hours. So $t=6$, and they left at 7:00 AM.