A runner is jogging in a straight line at a

Question

steady vr= 7.5 km/hr. When the runner is
L= 6.3 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vb= 22.5 km/hr (3 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.
016 (part 2 of 2) 10.0 points
After this first encounter, the bird then turns
around and flies from the runner back to the
finish line, turns around again and flies back
to the runner. The bird repeats the back and
forth trips until the runner reaches the finish
line.
How far does the bird travel from the beginning (including the distance traveled to the
first encounter)?
Answer in units of km.

Answer 1

part 2 is easier than part 1
The runner takes 6.3/7.5 = 0.84 hr to reach the finish line.
The bird flies all during that time at a speed of 22.5 km/hr
distance = speed * time, right?

For part 1, the bird takes 6.3/22.5 = 0.28 hr to reach the finish line
During that time, the runner has moved 7.5 * 0.28 km closer, so he is only 6.3-2.1 = 4.2 km from the finish line.
So now find when the runner's distance and the bird's distance adds up to 4.2 km
4.2 - 7.5t = 22.5t
Then add that distance to the bird's starting 6.3 km