The “5 seconds after they started moving” is relevant. If we assume this takes place on Earth (i.e. on the surface of a sphere with a set pair of north/south poles), the angle between the two vectors changes depending on their current position.

If it's not on the equator, it's also slightly up to interpretation if "Due East" means they'll turn to stay on the same latitude, always adjusting to stay moving east forever or if they'll do a great circle. In the former case, the north moving one will eventually get stuck at the north-pole too instead of continuing their circle around the globe. Most likely not within 5 seconds though, unless the place they started was within 25 feet of the north-pole.

To actually do the math we'll need to know (or somehow deduce) where "the place where everything about them began" is though.

I guess the calculus portion of this is to write the separation as a function of time, s = √26*t, and then realize that the rate of separation is the same regardless of time, because the first derivative is a constant.

I mean, there’s quite a few calculus problems that you can do without calculus. Pretty much 80% of the optimization problems/max’s and minimums in a typical Calc 1 class can be done if you remember that -b/2a is the vertex of a quadratic.

The boy's speed is given as 5 ft/sec, but the question is ambiguous as to whether his position remains due north of the starting point, or due north of the girl. Your approach assumes the former, but his 5ft/sec speed may include the girl's 1ft/sec eastward component.

i have the feeling that the kind of person that buys a car for his 16yo gf, is like the one that's leading the united states

What if I love your boyfriend?

You forgot about the curvature of the earth!

What about the local topology? What if she's walking uphill and he's running downhill?

No but if they’re in Mexico you gotta keep it’s sink rate in mind

thats what the unannounced bonus points are for

It's not how far apart they are It's how fast they are seperating. I'm not sure but the rate they are seperating might change as they get further apart due to the triangle or something? Otherwise yeah just a triangle.

They said goodbye at a given position and are then leaving each in a different direction. They start to move at the same time from the same point.

(I don't even speak English every day anymore, so I could be wrong).

You're not wrong. I think some of it is the difference between casual speech and formal writing (people are more likely to say "after being" but write "after having been", especially in published work)**, but some of it is also just poorly phrased. It makes enough sense to a native speaker to get what the problem is asking, though.

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** I think the first may be correct in some cases, but idk the rule.

One of my game development lecturers always used giving handjobs to stakeholders as an example of balancing priorities and keeping everyone happy while being pulled in multiple directions. I'm assuming someone complained though because when I had him for a different class he'd stopped.