A runner is jogging at a steady 3.9 km/hr.
When the runner is 7.4 km from the finish
line, a bird begins flying from the runner to
the finish line at 19.5 km/hr (5 times as fast
as the runner). When the bird reaches the
finish line, it turns around and flies back to
the runner.
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
the runner and the bird travel for the same amount of time
the bird travels five times as fast as the runner, so it covers five times the distance
5 * 7.4 km = ?
To find out how far the bird travels from the beginning, we need to calculate the distance it covers during each round trip it makes between the runner and the finish line.
First, let's determine how long it takes for the bird to reach the first encounter point. The distance the runner has already covered is 7.4 km, and the bird flies at a speed of 19.5 km/hr. Using the formula "distance = speed * time," we can rearrange it to find the time it takes for the bird to cover this distance:
time = distance / speed
time = 7.4 km / 19.5 km/hr
time ≈ 0.379 hours (rounded to three decimal places)
Now that we know the time taken for the bird to reach the first encounter, we can compute the distance it travels during that time. Since the bird flies at a speed of 19.5 km/hr, the distance it covers during 0.379 hours is:
distance = speed * time
distance = 19.5 km/hr * 0.379 hr
distance ≈ 7.3965 km (rounded to four decimal places)
Therefore, the bird travels approximately 7.3965 km from the beginning, including the distance traveled to the first encounter.