SOLUTION: an airplane leaves chicago at noon and travels south at 500 mph. another airplane is traveling east towards chicago at 650 miles per hour and arrives at 2pm. when were these two

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: an airplane leaves chicago at noon and travels south at 500 mph. another airplane is traveling east towards chicago at 650 miles per hour and arrives at 2pm. when were these two       Log On


   

Question 919434: an airplane leaves chicago at noon and travels south at 500 mph. another airplane is traveling east towards chicago at 650 miles per hour and arrives at 2pm. when were these two airplanes closest to each other, and how far apart were they at that time?
used a^2 + b^2 = c^2
using derivatives and implicit derivative. I am stuck... Please help.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Define t: = number of hours past 12pm, so the first plane is 500t miles S of Chicago, and the second plane is 650(2-t) miles E of Chicago. The distance D is


Instead of minimizing D, you can minimize D^2 which will make the problem easier (D^2 will be a quadratic in terms of t). You can take the derivative and set to zero to find the maximum, or use the fact that the vertex of the quadratic occurs at .