At noon, ship A is 100km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25km/hr. How fast is the distance between the ships changing at 4.00pm.

• Let the position of ship B at noon be at the origin
  =>ship A has x-coordinate = -100km and B has x-coordinate =0km
  At 4.00 p.m., ship A is at x = -100+4*35=40km
  and B is at x = 0 and y = 4 * 25 = 100 km
  Distance between them at 4.00 p.m. = √[(100)^2 + (40)^2] = 20√(29) km
  
  Distance between the ships,
  s^2 = x^2 + y^2
  => 2s ds/dt = 2x dx/dt + 2y dy/dt
  => rate of change of distance between the ships, ds/dt
  = (x dx/dt + y dy/dt) / s
  = [40 * 35 + 100 * 25] / [20√(29)] km/hr
  = (1400 + 2500) / [20√(29)] km/hr
  = 195/√(29) km/hr
  ≈ 36.21 km/hr.
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