[ QUOTE ]
This is gonna sound really patronising but, ... what a brilliant question!
[/ QUOTE ] Agreed. But I am surprised that no-one has asked the question that this one begs.
It is reasonable to suppose that A and B are in radio communication, or similar (otherwise how would A know B's position, course and speed?) It is also reasonable to suppose that both parties are keen to meet. In real life, therefore, B might feel it churlish to insist on maintaining his present course and speed if he could make an alteration to expedite the meeting.
Let's suppose they're not in a tearing hurry to meet (and rule out the fastest meeting time which is achieved by heading straight at each other), but instead want to meet at some time before their joint objective, called C.
The iterative technique becomes impossibly complex for this question, unless you run a computer program. A more practicable approach is to look at the positions on a chart, choose a promising-looking meeting time (say 3 hours) and draw circles around A and B with radii corresponding to the distances they expect to travel in 3 hours. If the intersection of the circles, D1, (rendezvous proposal 1) involves unacceptable course alterations, alternative proposals D2, D3 etc can be plotted based on 4 hours, 5 hours, etc. sailing.
No - they are not in radio contact. Not until within 10-15 miles anyway, but see below.
Picture this. Boat A is anchored somewhere in the west of Lyme Bay and gets a text from boat B (actually from swmbo.B) "just departed Chebourg for Aber Il'duit. F4 NW expect mostly reachy. Expect 26 hrs. See you there. You are buying".
swmbo.A says "We must leave now and meet them on the way." In the hour of frank discussion and hasty passage planning that follows boat B goes out of texting range.
Anything other than an unannounced looming up out of the morning mist on a precise intercept course will result in a glum swmbo. The sort of glumness that spreads.
(this is a senario. any resemblance with any persons living or dead is unintended, honest)
There are many circumstances in today's 'yottie' world where some of these traditional nav-plotting techniques are still valid, still have a role to play.
There was quite a lot of interest in this one. Lets' explore another one, in a fresh thread....
Keyword - 'Critical Point' - but may I suggest first thinking through the relevant considerations?
It's question like this that reminds me I must take my aviation circular slide rule with me when I go sailing. Great bits of kits that make calculating headings and ground speeds a doddle to calculate and this problem can be solved in moments without having to plot a thing. OK the mach speed calculator is not much use, but it isn't much use in a helicopter either.