The maneuvering board is just a piece of paper with a polar plotting grid printed on it. For the problem you describe, all you need do is to put your vessel at the center and plot your friends range and bearing from you. That wil establish the initial relative positions of both boats.
Now, plot a vector representing the course and speed of your friend's boat, originating at the center of the plot. Draw a line parallel to the his relative bearing from you and long enough to intersect the circle that represents your vessel's speed. The intersections thus drawn will be at the courses that will give (1) best closing speed, and (2) best opening speed relative to your friend.
There are also other techniques that allow you, for example, to estimate course and speed of another vessel from its observed relative motion.
The principles are especially useful when using radar because of its ranging capability.
