At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 24 knots and ship B is sailing north at 22 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.)

Answer 1

did you make a diagram,
that is essential in these type of questions.

let the time be t hours after noon.
In my diagram I have a right-angled triangle with the base as (40 + 24t) and a height of 22t

let s be the distance between them

s^2 = (40+24t)^2 + (22t)^2 (equation #1)

then 2s(ds/dt) = 2(24)(40+24t) + 2(22)(22t) (equation #2)

use t=4 in #1 to find s, then use
that s and t=4 in #2