calc
posted by angel on .
A____________B 9 miles is between A and B?
at 3pm Andy began travelling South at a rate of 4mi/hr from point A
at the same time Bill began travelling West at a rate of 5mi/hr from point B to A
both stop wlking when Bill reaches point A
What time will the distance between Bill and Andy be minimized?

Let A be (0,0) and B = (9,0)
The distance d between Bill and Andy after h hours can be found using
d^2 = (4h)^2 + (95h)^2
= 16h^2 + 81  90h + 25h^2
= 41h^2  90h + 81
d = √(41h^2  90h + 81)
dd/dh = (82h  90)/√(41h^2  90h + 81)
dd/dh = 0 when h = 90/82 = 1.1 hr = 1:06
3:00 + 1:06 = 4:06