A runner is jogging at a steady 4.8 km/hr.

When the runner is 6.3 km from the finish
line, a bird begins flying from the runner to
the finish line at 14.4 km/hr (3 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

The following question is part 2

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.

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

First, let's calculate the time it takes for the bird to reach the finish line. We can use the formula:

Time = Distance / Speed

For the bird, the distance is 6.3 km (the distance from the runner to the finish line) and the speed is 14.4 km/hr. Therefore:

Time taken to reach the finish line = 6.3 km / 14.4 km/hr = 0.4375 hours

Next, let's calculate the time it takes for the bird to return to the runner. Since the bird is flying back at the same speed, the time will be the same as before:

Time taken to return to the runner = 0.4375 hours

The total time the bird takes for one round trip (from the runner to the finish line and back to the runner) is:

Total time for one round trip = Time taken to reach the finish line + Time taken to return to the runner = 0.4375 hours + 0.4375 hours = 0.875 hours

Now, let's calculate the distance the bird travels in one round trip. The bird is flying at a speed of 14.4 km/hr for a total time of 0.875 hours:

Distance traveled in one round trip = Speed x Time = 14.4 km/hr x 0.875 hours = 12.6 km

Therefore, the bird travels a distance of 12.6 km in one round trip.

Moving on to part 2 of the question, we need to calculate the total distance the bird travels from the beginning until the runner reaches the finish line.

Since the bird travels a distance of 12.6 km in one round trip, we can divide the total distance between the runner and the finish line (6.3 km) by the distance traveled in one round trip (12.6 km) to find the number of round trips the bird makes.

Number of round trips = Total distance / Distance per round trip = 6.3 km / 12.6 km/round trip = 0.5 round trips

Notice that the result is 0.5 round trips. This means the bird completes one round trip, and when it returns back to the runner, the runner reaches the finish line. Therefore, the bird only makes one complete round trip.

The total distance the bird travels from the beginning (including the distance traveled to the first encounter) is equal to the distance traveled in one round trip:

Total distance traveled by the bird = Distance per round trip = 12.6 km

Therefore, the bird travels a distance of 12.6 km from the beginning (including the distance traveled to the first encounter).