# Thread: related Rates problem

1. ## related Rates problem

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?

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?
Code:
            P   5t    A
* - - - - *
|
|
30 |
|
|
* Q
/
/
10t/
/
/
B *

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.