At noon, ship A is 100km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 15km/h. How fast is the distance between the ships changing at 4:00pm?

Answer 1

At a time of t hrs,
let the position of ship A be P and let the position of ship B be Q
Join PQ, and complete the large righ-angled triangle
having a base of 100 and a height of 15t + 30t or 45t
(the horizontal distance between them is always 100 km
PQ^2 = 100^2 + (45t)^2

2 PQ d(PQ)/dt = 0 + 2(45t)(45)
d(PQ)/dt = 2025t/D

at 4:00 , t = 4
PQ = √(100^2 + 180^2) = appr 205.913

d(PQ)/dt = 2025(4)/205.913
= 39.34 km/h