Two friends A and B leave point A and point B simultaneously and trave

Dear alphonsa,
I'm happy to respond. Something seems flawed with the question, or at least unclear. First of all, I think the word "respectively" is implied by not stated in the first sentence --- that would clear up a certain amount of the ambiguity. From the first sentence, I picture a line, AB. Traveler A starts at A and moves toward B. Traveler B starts at B and moves toward A. So far so good. The completely unclear part of the question is: how on earth do these travelers "meet along the route at two points"? If one goes from A to B, and the other from B to A, then they will cross paths just once, as they passed each other. For them to meet twice --- the route must be more complicated, or each one goes in both directions, or something of that sort. That one condition throws everything about the entire scenario into doubt.

If each one travels a straight line, A to B, and B to A, and they cross paths only once, at one point, then it's a relatively straightforward problem.

The meeting point m divides the total distance into two lengths, which I will call K and L.

Call the time it takes them to meet at the meeting place T.
In that time T, A covers the distance K, and B covers the distance L. Thus
K = (vA)*T
L = (vB)*T
They meet at m, and keep moving. After the meeting, A covers the distance L is 32 minutes, and B covers the distance K in 50 minutes.
L = (vA)*32
K = (vB)*50
Set the expression for the distance equal.
(vA)*T = (vB)*50 and (vB)*T = (vA)*32
Rewrite each equation to equal the ratio of (vA)/(vB)
(vA)/(vB) = 50/T
(vA)/(vB) = T/32
Set these equal and solve for T
50/T = T/32
T^2 = 50*32 = 100*16 = 1600
T = 40
So B traveled 40 minutes along L and 50 minutes along K for a full time of 90 minutes. Answer = (B).

Notice that I used the doubling & halving trick to multiply 32 times 50. See:
https://magoosh.com/gmat/2012/doubling-a ... gmat-math/

That's what happens if the two travelers meet at one point during this process. If they meet at two points, I have no earthly clue what paths they have taken.

Does all this make sense?
Mike