A jet flying due north at 640 mi/hr passes over this town at noon. 15 minutes later another jet flying due west passes over the same town. The planes are flying at the same altitude. At what time will they be separating at 872 mi/hr?

(edited) The answer is 1:15 p.m.

I tried. I think I must be missing something very simple.

Drew the figure, a right triangle with the right angle in the lower right hand corner. Distance y (vertical leg) represents distance covered by the 640 mi/hr jet and the distance x (horizontal leg) represents distance covered by the 600 mi/hr jet, and distance r (hypotenuse) the distance between the two jets.

... courtesy of Pythagoras

... differentiated

I believe my knowns are

I was thinking that I need to find in hours, and that I should be able to set it up like this:

The x-distance would be

and the y-distance would be

making the r-distance

Plugging everything into the 1st derivative equation above,

(edited) This should have worked out so that . Then we add that, (in the form of 1:15) to 12:00 noon and get 1:15 p.m.

Alas, things got gnarly when I tried to solve the above equation. What am I missing? Is there a way on this one to "work smarter, not harder?"