Two planes leave an airport simultaneously. One travels north at 300 mph and the

Question

other travels west at 400 mph. How fast is the distance between them changing after 10 minutes?

Answer 1

Using a scaled-up 3-4-5 triangle, the distance after 10 minutes is 1/6 (500) miles.

If z is the distance between them after t hours, then

z^2 = (300t)^2 + (400t)^2
z dz/dt = 2*300^2 t + 2*400^2 t

Now just plug in your numbers with t = 1/6