The lookout on board a ship spots an unknown ship on the open seas and immediately alerts Chris, the ship's captain. The unknown ship is currently 4 miles south and 3 miles east of Captain Chris's ship, and it is at that moment sailing due west at 20 mph. Captain Chris's ship, meanwhile, is at the moment sailing due north at 16 mph. Is the distance between Captain Chris's ship and the unknown ship increasing or decreasing? How fast? (distance is measured along a straight line joining the two ships.)

Question

anonymous · Answer

Helpful tip: Draw a picture of the two ships.

anonymous · Answer

As in a right triangle such as this?
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anonymous · Answer

Yup, but add a coordinate system to it. you also know U is moving west at 20 mph and C is moving north at 16 MPH. Knowing that we can make an equation. so let t be number of hours. Chris' location will be (0,16t+4) after t hours. 
For the unknown ship, U at 0 hours would be (3,0) 
U(t) is (3-20t,0)
What do you think you can do to find the distance between U(t) and C(t)? That distance would be d(t). Also what do you know if the derivative, d(t) is positive? What does it tell you about the distance between U and C? What if d(t) is negative? 
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