At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 20 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.)

Question

Note: Draw yourself a diagram which shows where the ships are at noon and where they are "some time" later on. You will need to use geometry to work out a formula which tells you how far apart the ships are at time t, and you will need to use "distance = velocity * time" to work out how far the ships have travelled after time t.

Answer 1

Following your note, I made a diagram and let the time at "some time" later be t hours.
I see a right-angled triangle.
Let the distance between them be D nmiles.

D^2 = (16t)^2 + (50+20t)^2
2D(dD/dt) = 2(16t)(16) + 2(50+20t)(20)
dD/dt = (656t + 1000)/D

At 6:00, t=6
D^2 = 38116
D = 195.2332

dD/dt = (656(6) + 1000)/195.2332
= 25.28 knots

check my arithmetic.

Answer 2

25.28

Answer 3

fools

= 82.52

Answer 4

It's definitely 25.28