Question

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 18 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

let t hours be some time past 12:00 noon

After t hours, ship B has gone 20t knots
and ship A has gone 17t knots

let the distance between them be D
I see a right-angled triangle and
D^2 = (20t)^2 + (17t+10)^2
D^2 = 689t^2 + 340t + 100
2D(dD/dt) = 1378t + 340
dD/dt = (689t + 170)/D

at 4:00 pm, t=4 and
D^2 = 12484
D = 111.7318

so at t=4
dD/dt = (689(4) + 170)/111.7318
= 26.19 knots

Answer 2

This is not the right answer