At noon, ship a is 60 km west of shipb. ship a is sailing south at 15 km/h and ship b is sailing north at 5 km/h. how fast is the distance between the ships changing at 4:00 pm?

dA/dt=15 km/h and dB/dt=5 km/h
base of our triangle if drawn is 60 km
to find dD/dt when t=4 hours we shall have:

(A+B)²+60²=D²
d/dt[(A+B)²+60²]=d/dt(D²)
[d(A+B)]/dt*2(A+B)(2)=dD/dt*2D
B=5km/h*4hr=20km
A=15km/hr*4=60km
20²+60²=D²
D=√4000

(15+5)*(2)*80*(2)=2*√4000*dD/dt
dD/dt=6400/√4000=101.192 km/hr