Optimization Problem - # 3

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Jason76

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Oct 19, 2012
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A boat leaves a dock at 5:00 PM 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 6:00 PM. How many minutes after 5:00 PM were the two boats closest together? (Round your answer to the nearest minute.)

Some ideas on how to get this setup? I know the Pythagorean theorem will be used, and a derivative will be taken.
 
Yes, that's correct- so do it! The first boat is moving away from the dock at 20 mph so its distance from the dock, t hours after 5:00, is 20t. The second boat is moving toward the dock at 15 mph and reaches the dock at 6:00, t= 1. The second boat's distance from the dock is given by 15- 15t (at 5:00, t= 0, the boat is 15 m from the dock, at t= 1, it is at the dock). Use the Pythagorean theorem to write a formula for the distance between boats as a function of t.
 
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