At 5 P.M. an oil tanker traveling west in the ocean at 16 kilometers per hour pa

Question

At 5 P.M. an oil tanker traveling west in the ocean at 16 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 4 P.M. while traveling north at 19 kilometers per hour. If the "spot" is represented by the origin, find the location of the oil tanker and the location of the luxury liner t hours after 4 P.M. Then find the distance D between the oil tanker and the luxury liner at that time. D(t) = _______ At what time were the ships closest together? (Hint: Minimize the distance (or the square of the distance!) between them.) The time is ___:___ P.M. (Round down to the nearest minute.)

Explanation / Answer

imagine the "spot" or origin is point 0,0 on a graph and the oil tanker is traveling right along the x axis while the liner is traveling up the y axis this will create a right triangle when you measure how far apart the two ships are the base will be how far the tanker traveled since 5pm at a speed of 16 so its distance will be 16t the liner had a 1 hour headstart as it headed north at a speed of 19 so its distance is 19 multiplied by (t +1) or 19(t+1) so lets use 2 hours as an example the bottom of your triangle is 16t or (16 x 2 ) or 32 the other side is 19(t+1) or (19 x 3) or 57 so at 8 o'clock or 2 hours you have a triangle you can use Pythagorean to find the value..

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