Related Rates Calculus

Question

Two airplanes fly eastward on parallel courses 12 km apart. One flies at 240km/h and the other at 300km/h. how fast is the distance between them changing when the slower plane is 5km farther east than the faster plane?

Answer 1

D = sqrt(12^2 + (60t)^2), with the current time being t = -5/60

dD/dt = 120t*60(1/2)/sqrt(12^2 + (60t)^2) = 3600t/sqrt(12^2 + (60t)^2)

3600(-5/60)/sqrt(12^2+(60*-5/60)^2) = -300/sqrt(12^2+(-5)^2)) = -300/sqrt(144+25) = -300/13