math

Using the Pythagorean Theorem, the distance between the ships, (r), at 4PM =

[140 - 4(30)]² + [4(20)]² = r²

[140 - 120]² + [80]² =

[20]² + [80]²  =

400 + 6400 = 

6800 = r²

√6800km = r

And using

r² = x² + y²   where x = 20, y = 80 and r = √6800   and differentiating for time, we have

2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)

r(dr/dt) = x(dx/dt) + y(dy/dt)

Note that, if we consider x, y and r to be sides of a triangle, then (dx/dt) = -30km/hr  and (dy/dt) = 20km/hr

√6800km(dr/dt) = 20km(-30km/hr) + 80km(20km/hr)

√6800km(dr/dt) = -600km²/hr + 1600km²/hr

√6800km(dr/dt) = 1000km²/hr

(dr/dt) = [1000/√6800km]km²/hr ≈ 12.13 km/hr