How fast is their distance apart increasing?

let distance be x , y , distance between = z

z^2 = (x^2 + y^2)

z = √(10^2 + 40^2) = 10√17 miles

2zz' = 2xx' + 2yy'

z' = (xx' + yy')/z

z' = (10 * 15 + 40 * 30)/(10√17)

z' = (150 + 1200)/ (10√17)

z' = 135/√17 ≈ 33 mph

let us consider first quadrant . take x axis as east and y axis as north

define a function z = x/40 + y/10 [ equation of line joining two points]

differentiate z w.r.t time

dz/dt = dx/dt(1/40) + dy/dt(1/10) [ this gives sereration rate]

as dx/dt = 30 miles/hour

and dy/dt = 15 miles/hour

so dz/dt = 30/40 + 15/10

dz/dt = 0.75 + 1.5

dz/dt = 2.25 miles/hour

dz/dt = 2 miles/hour ( rounded value)