Relative Speed Questions

A ship develops a leak $20\text{ km}$ from the shore. Despite the leak, the ship is able to move towards the shore at a speed of $12\text{ km/hr}$. However, the ship can stay afloat only for $23\text{ minutes}$. If a rescue vessel were to leave from the shore towards the ship and it takes $8\text{ minutes}$ to evacuate the crew and passengers of the ship, what should be the minimum speed of the rescue vessel in order to be able to successfully rescue the people aboard the ship?

X gets on an elevator at the $11\text{th}$ floor of a building and rides up at the rate of $57$ floors per minute. At the same time, Y gets on an elevator at the $51\text{st}$ floor of the same building and rides down at the rate of $63$ floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?