let the horizontal distance is x and vertical distance is y and the distance between them is z z^2 = x^2 + y^2 2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt) divide by 2 z(dz/dt) = x(dx/dt) + y(dy/dt) when y = 45 , x = 0 because the boy was under the balloon after 3 secs: x = 15 * 3 = 45 , y = 5 * 3 = 15 , z = sqr(x^2 +y^2) = 75 z(dz/dt) = x(dx/dt) + y(dy/dt) 75(dz/dt) = 45(15) + 15(5) = 975 dz/dt = 13 ft/sec
