That's a useful technique, but doesn't respond directly to the problem as stated.
This is because there is no fixed time (time desired) for meeting. Rather, the desired meeting time is the EARLIEST time possible, given the relative positions of the vessels, the (fixed) course of one of them, and their respective speeds.
It's a classic intersect problem used in war gaming and targeting, as well as air and maritime navigation. Maneuvering Boards were the classic way to solve the problem, and a few brave souls used trig, but now calculators and computers make it easy.