At 5 P.M. an oil tanker traveling west in the ocean at 12 kilometers per hour pa

Question

At 5 P.M. an oil tanker traveling west in the ocean at 12 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 20 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. (1) D(t)=_______ . (2) 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 6pm at a speed of 18 so its distance will be 18t the liner had a 1 hour headstart as it headed north at a speed of 33 so its distance is 33 multiplied by (t +1) or 33(t+1) so lets use 2 hours as an example the bottom of your triangle is 18t or (18 x 2 ) or 36 the other side is 33(t+1) or (33 x 3) or 99 so at 8 o'clock or 2 hours you have a triangle

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