This is a 3-dimensional problem.
I hope I can explain it clearly.
A bridge is 30ft above a canal.
A motorboat going 10 ft/s passes under the center of the bridge
at the same instant that a man walking 5ft/sec reaches the point.
How rapidly are they separating 3 seconds later?
P 5t A
* - - - - *
At t = 0, the man is at point P.
. . t seconds later, he has walked 5t feet to point A.
At t = 0, the boat is at point Q.
. . t seconds later, it has moved 10t feet to point B.
The distance AB = z is the diagonal of a "box" with dimensions: 5t, 10t, and 30.
. . . . . . . . . . . . ._________________ . . . .__________
. . Then: . z .= .√(5t)² + (10t)² + 30² .= .√125t² + 900
Differentiate with respect to time and substitute t = 3.