I should begin by saying that I have never wondered this before. A relatively easy way occurs to me though assuming that you have and use paper charts. Plot your friend's position, and his course. Next mark of where you expect him to be in .5 hours, one hour, 1.5 hours etc, using a compass and your scale from the chart. Plot your position. Then use the compass to draw arc segments to show where you can be in half hour increments. At some point they should come very close to coinciding, and you can plot a course to that point.
Any better ways?