A runner is jogging in a straight line at a
steady vr= 2.1 km/hr. When the runner is
L= 4.4 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vb= 10.5 km/hr (5 times as fast as
the runner). When the bird reaches the finish
line, it turns around and flies directly back to
the runner.

What cumulative distance does the bird
travel? Even though the bird is a dodo, assume that it occupies only one point in space
(a “zero” length bird), travels in a straight
line, and that it can turn without loss of
speed.
Answer in units of km.

I've been having so much trouble it isn't even funny

So how long does it take the bird, going 10.5 km/hr to go 4.4 km. Equation for this is pretty simple. v = d/t, solve for t you get t = d/v. Then keep in mind the bird heads backwards after reaching the finish line without taking any time to turn around

The jogger keeps getting closer to the finish line as the bird does, so we want to know where he is after t time passes. so same formula, just rearrange it for d, d=vt. Then subtract that from 4.4 km to find how close the jogger is to the finish line after that much time. so 4.4-d.

We want to know when the two will meet, so a time For this you want to know that for two objects moving toward each other, from the point of view of one of the objects, it looks like the other is moving toward it at their two speeds added together. So we could say the jogger is standing still and we want the time it takes the bird, now moving at 10.5 + 2.1 km/hr to reach them. and we know the distance between them now is that 4.4-d. So using the same equation again solving for t we get d/v = (4.4-d)/(10.5+2.1). We'll call this tb to keep things organized.

With the time, we can find how far the bird went to get back. You could also use the time to see how far the jogger ran and make sure they meet in the middle of the new distance Anyway, same equation again. d = vt = 10.5*tb.

It's a loooooooot of plugging in and stuff, but hopefully that makes sense. Also, keep in mind we figured out the distance from the finish line to where the two would meet. The bird also flew from the original starting position 4.4 km away from the finish line. So we want to add these two distances. And that is the total distance the bird goes.

Let me know if I didn't explain anything well enough and hopefully I can improve.