Math!
posted by <3 .
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

I assume you made a diagram.
let the time passed since noon be t hours
in that time ship A has traveled 25t nmiles , and ship B has traveled 16t nmiles
let the distance between them be d nmiles
I see a rightangled triangle with base of
50 + 25t, a height of 16t and a hypotenuse of d
d^2 = (50+25t)^2 + (16t)^2
at 6:00 pm, t = 6
d^2 = 221.847
2d(dd/dt) = 2(50+25t)(25) + 2(16t)(16)
so at 6:00 pm
dd/dt = [2(50+150)(25) + 2(96)(16)]/221.847
= 58.923
check my arithmetic 
This answer isn't right either & I don't understand how you got d^2 = 221.847.

that d^2 = 221.847 was a typo
should have said d = 221.847
As you can see further down I used it as such.
Alos in my third last line of my previous post I should have divided by 2(221.847) to get
29.46 instead of 58.923 
Yeah. That's better. Thanks again!