<p>two ships leave a port at noon. one ship sails north at 6 miles per hour and the other sails east at 8 miles per hour. at what rate are the two ships seperating 2 hours later?</p>
<p>OK... so one ship is sailing east while the other one is traveling north and they give you the travel rates of the two ships. What you basically have to do is differentiate the Phytagorean Theorem(since their distance separation forms a right angle triangle) and then plug in the values for where each ship will be in 2 hours to get the rate of separation.</p>
<p>a^2+b^2=c^2
2a(da/dt)+2b(db/dt)=2c(dc/dt)</p>
<p>2 hours later...</p>
<p>2(12)(6)+2(16)(8)=2(10)(dc/dt)
dc/dt=20mi/hr</p>
<p>Hope my explanation made sense. PM me if you have any doubts and others can check my reasoning if my work is incorrect.;)</p>
<p>ahhh you make it seem so simple my friend</p>
<p>In the above analysis c = 20 after 2 hours, not 10</p>
<p>thanks for the help guys, anyone kind enough to solve this one</p>
<p>a shark, looking for dinner, is swimming parallel to a straight beach and 90 feet offshore. the shark is swimming at the constant speed of 30 feet per second. at time t=0, the shark is directly opposite a lifeguard station. how fast is the shark moving away from the lifeguard station when the distance between them is 150 feet?</p>
<p>These notes are amazing for Calc. Check the related rates section and it will explain it in very simple terms. </p>
<p><a href="http://tutorial.math.lamar.edu%5B/url%5D">http://tutorial.math.lamar.edu</a></p>
<p>thanks postmaster</p>
<p>holy **** those notes are awesome.. wish I had them when I was doing surface integrals... will definitely refer to them next term in diff eq (the instructor supposedly can't speak english according to ratemyprofessor.com haha)</p>
<p>thanks postmaster!</p>
<p>You're welcome :) Glad I could help :):):)</p>