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?
4t | *
A * *
1200 | *
P * - - - - - - - - - * - - - * Q
: * |
5t : * | 5t
: * |
R * - - - - - - - - - - - - - * W
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.
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!