You are ﬂoating on a block of ice in the middle of the ocean:

* The ice melts at a rate inversely proportional to the amount of ice present.
* There is an island $1000$ meters away, so you start paddling your block of ice toward the island. When you start paddling, there are $2$ cubic meters of ice.
* After paddling for $10$ minutes, there are $1.7$ cubic meters of ice, and you have traveled $250$ meters.

1. Find a diﬀerential equation describing the amount of ice as a function of minutes after you start paddling.
2. Solve the diﬀerential equation to determine how long after you start paddling it takes for the ice to completely melt.
3. Did you make it to the island before the ice melted away $?$.