
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 7,475 Thanks: 886 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: 7,475 Thanks: 886 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: 16,942 Thanks: 1253 
That geometrical approach works. What do you get if you try it and do the diagram you suggested?


Tags 
distance, shortest 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
shortest distance between 2 lines in 3space  Jimi  Algebra  2  November 4th, 2013 01:21 AM 
shortest distance between point and surface  Robert Lownds  Applied Math  2  May 17th, 2013 03:42 AM 
Shortest distance triangle  bracke  Algebra  3  May 10th, 2012 09:44 AM 
The shortest distance from Point A to the line...  DPXJube  Algebra  3  January 24th, 2011 06:53 PM 
shortest distance  arun  Algebra  6  March 4th, 2007 10:01 AM 