Point A is at (9,0) and moving towards the origin at 3 units/sec. Point B is at (0,6) and moving away from the origin at 2 units/sec. One second later, how fast is the distance between the points changing (units/sec)

Point A's coordinates at time t are (9 - 3t, 0), and point B's coordinates are (0, 6 + 2t).

The distance d between the two points at time t is

d(t) = √((9 - 3t)² + (6 + 2t)²) = √(13t² - 30t + 117)

so that at t = 1, the distance between the two points is 10.

The distance changes at a rate of

dd/dt = (26t - 30) / √(13t² - 30t + 117) units/sec

so that at t = 1 sec, the distance is changing at a rate of

dd/dt (1) = -1/5 units/sec