Question

At noon, Al is 6km north of point O traveling south at 10km/h. Also at noon, Barb is 2km east of point ) traveling east at 5km/h.

A) express the distance "d" between Al and Barb as a function of time "t" hours after noon.
B) Find the time at which the distance is a minimum

Answer 1

as usual, draw a diagram.
Al's distance a is 6+10t
Barb's distance b is 2+5t

d^2 = (6+10t)^2 + (2+5t)^2
= 5(25t^2 + 28t + 8)

Now just set dd/dt=0 to find the minimum.