Two people start at the same point One walks east at 2mph and the other walks southwest at 3mph. How fast is the distance between them changing after 30 minutes?

Answer 1

At a time of t hrs,
let the distance travelled by the eastbound person be 2t miles
and the distance of the other person be 3t miles
let the distance between them be d miles, and of course the angle between them is 135°
d^2 = (2t)^2 + (3t)^2 - 2(2t)(3t)cos135°
= 13t^2 - 12t^2(-√2/2)
= 13t^2 + 6√2 t^2

2d dd/dt = 26t + 12√2 t
dd/dt = (13t + 6√2 t)/d

plug in t = 1/2 or .5 into d^2 = ... to find d, then sub into dd/dt

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