A runner is jogging at a steady 2.3 km/hr.

When the runner is 8.4 km from the finish
line, a bird begins flying from the runner to
the finish line at 9.2 km/hr (4 times as fast
as the runner). When the bird reaches the
finish line, it turns around and flies back to
the runner.
How far does the bird travel? Even though
the bird is a dodo, assume that it occupies
only one point in space (a “zero” length bird)
and that it can turn without loss of speed.
Answer in units of km

To find out how far the bird travels, we need to calculate the time it takes for the bird to reach the finish line and return back to the runner.

Since the bird is 4 times faster than the runner, we can calculate the time it takes for the bird to reach the finish line using the formula:

Time = Distance / Speed

The distance the bird needs to cover is 8.4 km, and its speed is 9.2 km/hr.

Time = 8.4 km / 9.2 km/hr
Time = 0.913 hours

Now that we know the time it takes for the bird to reach the finish line, we can calculate the distance it travels in that time by using the formula:

Distance = Speed x Time

The speed of the bird is still 9.2 km/hr, and the time is 0.913 hours.

Distance = 9.2 km/hr x 0.913 hr
Distance ≈ 8.398 km

So, the bird travels approximately 8.398 km.