The large containership MS Titan has run aground at the southern entrance of a canal. Two tugboats are in the vicinity and are called for immediate help: the tugboat Atlas is exactly 80 kilometres south of the containership and the tugboat Hercules is exactly east of the Atlas and 160 kilometers away from the containership. Both tugboats start traveling directly towards the containership, the Atlas with a constant speed of 20 kilometres per hour and the slightly stronger Hercules at 30 kilometres per hour.
What is the rate of change of the distance between the Atlas and the Hercules at the moment when the Atlas is 40 kilometres away from the containership.
The approach I'm trying to do is using cosine rule to calculate angle a, which I believe it is a constant angle. I used Pythagorem Theorem to find x, which equal to $80\sqrt3$ km.
After that, using cosine law, I'm able to find out the angle a is a $60^o$ angle.
But from here, I'm unable to process furthermore because I think I'm lacking information, when y = 40, z and x must also change. So can anyone give me an idea of what should I do or help me with a better approach than this one. All help is really appreaciate