A runner is jogging at a steady 1 km/hr.
When the runner is 0.88 km from the finish
line a bird begins flying from the runner to
the finish line at 3 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. 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 did 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.
Possible answers:
1. 1.50 km ≤ db < 1.75 km 2. 2.75 km ≤ db < 3.00 km 3. 5.00 km ≤ db ≤ ∞ km 4. 3.00 km ≤ db < 5.00 km 5. 2.25 km ≤ db < 2.50 km 6. 1.75 km ≤ db < 2.00 km 7. 1.40 km ≤ db < 1.50 km 8. 1.30 km ≤ db < 1.40 km 9. 2.00 km ≤ db < 2.25 km 10. 2.50 km ≤ db < 2.75 km
(Please chose one of the possible answers)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
This was the answer:
2.50 km ≤ db < 2.75 km
To find out how far the bird traveled, we need to calculate the total distance it traveled during each round trip until the runner reached the finish line.
First, let's determine the time it takes for the runner to reach the finish line. The runner is jogging at a steady pace of 1 km/hr. The remaining distance to the finish line is 0.88 km. Using the formula distance = speed × time, we can rearrange it to solve for time.
time = distance / speed
Plugging in the values, we get:
time = 0.88 km / 1 km/hr = 0.88 hr
Now, let's calculate the distance the bird travels during each round trip. The bird flies from the runner to the finish line at a speed of 3 km/hr and back to the runner at the same speed. So, the bird's total speed is 3 km/hr + 3 km/hr = 6 km/hr.
Since the bird and the runner are both moving for the same amount of time, we can use the formula distance = speed × time again to calculate the distance the bird traveled during each round trip.
distance = speed × time = 6 km/hr × 0.88 hr = 5.28 km
As the bird goes back and forth with each round trip, it travels a distance of 5.28 km. However, we are asked to find the total distance the bird traveled until the runner reaches the finish line.
Since there is only one round trip before the runner reaches the finish line, the bird traveled a total distance of 5.28 km.
Therefore, the correct answer is 5.00 km ≤ db ≤ ∞ km (Option 3).
bird flying time ... 0.88 km / 1 km/h
bird distance = flying time * rate