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May 15th, 2010, 09:48 PM  #1 
Senior Member Joined: Sep 2008 Posts: 199 Thanks: 0  shortest distance
A boat leaves a dock at 3:00 P.M. and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 4:00 P.M. How many minutes after 3:00 P.M. were the two boats closest together? Attempt : the velocity A relative to B is 25. And in one hour, A travels 15 km to reach the dock. That's all I can decipher from the question. What else do I have to look into? 
May 15th, 2010, 10:06 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,600 Thanks: 942 Math Focus: Elementary mathematics and beyond  Re: shortest distance
Let the dock be the origin. Let the position of the ship heading east at 15 km/h be x. Let the position of the ship heading south at 20 km/h be y. x = 15  15t and y = 20t, where t is the time in hours. Can you take it from there?

May 15th, 2010, 10:54 PM  #3  
Senior Member Joined: Sep 2008 Posts: 199 Thanks: 0  Re: shortest distance Quote:
I thought the dock should be the point where both ships are heading towards?  
May 15th, 2010, 11:04 PM  #4  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,600 Thanks: 942 Math Focus: Elementary mathematics and beyond  Re: shortest distance
"A boat leaves a dock at 3:00 P.M. and travels due south . . ." implies the ship is headed away from the dock. "Another boat has been heading due east at 15 km/h and reaches the same dock . . ." implies the ship is headed towards the dock. I'll finish up using calculus: Let be the distance between the two ships. Take the derivative, set it equal to 0 to minimize: so the ships are closest together at minutes after 3:00. Quote:
 
May 16th, 2010, 01:00 AM  #5  
Senior Member Joined: Sep 2008 Posts: 199 Thanks: 0  Re: shortest distance Quote:
 
May 16th, 2010, 02:56 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,063 Thanks: 1396 
That geometrical approach works. What do you get if you try it and do the diagram you suggested?


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