In relativity time is no longer a universal concept, it is a quantity specific to a frame of reference. It isn't meaningful to compare the "age" of two objects in two different frames of reference using a single "frame time." "Frame time" denotes time as measured in a specific frame of reference. This frame of reference could be that of either object for example or perhaps even a third party observer. There is one way to compare ages of objects that's meaningful though but it requires a different concept of time to be measured. Proper time is the time measured in a frame of reference where the observer measures him or herself to be at rest. This definition is rather bizarre since it doesn't allow arbitrary points in space to have a proper time. Only observers with a defined velocity (or motion of any kind) can have a measured proper time. It is still a useful concept as it allows us to directly compare what different observers measure from their own frame of reference.
With your example we can use proper time to see how old the travelers are as measured in their own time. By the definition of proper time, traveler A and traveler B age in terms of proper time at the same rate, that's the whole point of proper time! Now what happens when they try to measure each other's age using their own time? If they do this they're not measuring the other traveler's age in terms of proper time, but rather their own frame time. They would need to calculate the proper time of the other traveler that they're observing. But when traveler A observes traveler B at a proper time of 1 minute, does traveler A see traveler B at a proper time of 1 minute or some other time? Obviously there will be some delay for the light of traveler B to reach A, but even accounting for this effect, do we expect A to still measure a difference in her observation of B's proper time? The answer is yes, we do, because A's notion of simultaneity is not the same as B's.
When A looks at B, A does not see B at the same proper time A sees herself. Because they are moving at different relative speeds, A's frozen snapshot of space at a given time doesn't look like B's. We could imagine depicting A's frozen snapshot of space as a line where at each point we give the value of A's clock for that point. It will look like this for A say at time = 0:
Every point exists at the same time. Now from B's perspective we could depict A's frozen time snapshot assigning those same points a time, t', based on B's clock instead. It will look like the following for example:
A's frozen time is frozen at a different time for each point in space from B's perspective. Likewise from A's perspective, B's frozen snapshot looks the same as A's did from B's perspective. This means measuring each other's age at a frozen snapshot is not a fair depiction of how A or B would measure their own age. A doesn't see B at her own value of proper time and likewise B doesn't see A at his own value of proper time. They are just as delayed from each other's point of view. This is the same thing as depicted in the graphic knzhou posted in the comments. The diagonal line of the driver represents B's simultaneity as seen from A. All along this line, A has different values of her clock even though it is a "frozen snapshot."
So what happens if A and B decide to meet in the same frame of reference, i.e. have 0 relative speed? Then they will have the same frame time and when they measure each other's proper time, it will match their own proper time. So what will their relative ages be? It depends on how they get there. If they both agree to do equal work to match speeds, they will see each other age the same amount over the time it takes to match speeds. If A does more of the work, then she will come out younger for it, if B does more of the work, then he will be younger.