Hello, FalconPUNCH!

Make a sketch!

1) A man starts walking north at 4ft/s from a point P.

Five minutes later a woman starts walking south at 5ft/s from a point 500ft due east of P.

At what rate are the people moving apart 15 min after the woman starts walking? Code:

M *
| *
4t | *
| *
A * *
| *
| *
1200 | *
| *
| *
P * - - - - - - - - - * - - - * Q
: * |
5t : * | 5t
: * |
R * - - - - - - - - - - - - - * W
500

The man starts at P and has a 5-minute headstart.

In 5 minutes (300 sec), he walks 1200 feet to point A.

In the next seconds, he walks ft to point M.

The woman starts at Q and walks south at 5 ft/s.

In the next seconds, she walks ft to point W.

Let

In right triangle MRW, we have: .

. . That is: . 4t+1200 + 5t)^2 + 500^2 \:=\9t+1200)^2 + 500^2" alt="x^2\:=\4t+1200 + 5t)^2 + 500^2 \:=\9t+1200)^2 + 500^2" />

Differentiate with respect to time: .

. . Hence: .

In 15 minutes,

Find at that time, and you're done!