See below and answer both questions fully. A runner is jogging at a steady 4.6 k

Question

See below and answer both questions

fully.

A runner is jogging at a steady 4.6 km/hr. When the runner is 7.3 km from the finish line, a bird begins flying from the runner to the finish line at 18.4 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 km 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

Explanation / Answer

1. time taken by the bird to reach the finish line = distance / speed = 7.3 km/ 18.4 km/hr = 7.3/18.4 hr

by this time the runner would have travelled a distance = speed * time = 4.6 km.hr * 7.3/18.4 hr = 7.3/4 km

now , at this moment the distance between runner and the bird = 7.3 km - 7.3/4 km = 3/4 * 7.3 km

they both are now moving towards each other to cover this remaining t=distance before they encounter for the first time.

since the bird is moving 4 times faster , it covers 4 times more distance than runner.

so distance covered by bird = 4/5 * distance = 4/5 * (3/4 * 7.3 ) km = 3/5 * 7.3 km

total distance covered by the bird = 7.3 km + 3/5 * 7.3 km = 11.68 km

2. time it takes for the runner to reach the finish line = distance / speed = 7.3 km / 4.6 km/hr = 7.3/4.6 hr

in this entire time the bird keeps on moving with speed 18.4 km/hr back and forth.

so total distance covered by the bird = speed * time = 18.4 km/hr * 7.3/4.6 hr = 29.2 km

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