.Two hikers begin at the same location and walk in perpendicular directions. Hiker A travels due north at a rate of 3 miles per hour; Hiker B travels due east at a rate of 5 miles per hour. At what rate is the distance between the two hikers changing 4 hours into the hike?

Answer 1

let the time passed be t hours

Simple right-angled triangles

let the distance between them be D
D^2 = (3t)^2 + (5t)^2
D^2 = 34t^2
D = √34 t
dD/dt = √34

So the distance between them is changing at a constant rate of √34 mph, independent of the time