At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 24 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.)

Answer 1

Make a sketch by placing B at O, the origin of the x-y plane, and A at (-50,0)

After t hours, A will be 50 + 23t nautical miles west from O, and B will be 24t nmiles north of O
Sketch the right-angled triangle and let d be the distance between them
d^2 = (50+23t)^2 + (24t)^2
2d dd/dt = 2(50+23t)(23) + 2(24t)(24

when t = 4
d^2 = 20164+9216
d = √29380

dd/dt = ( 2(50+23t)(23) + 2(24t)(24) )/(2d)
divide the right side by 2, sub in t = 4 , and d = ....

let me know what you got, so we can compare answers