At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) Please help!

Answer 1

At time t=0,
A is at (-30,0)
B is at (0,0)

At any later time t,

A is at (-30-23t,0)
B is at (0,17t)

So, the distance between the ships is

d^2 = x^2+y^2
d dd/dt = x dx/dt + y dy/dt

At 4:00,
x = 30+4*23 = 122
y = 4*17 = 68
d = 139.67
dd/dt = (122*23 + 68*17)/139.67 = 28.37