Question

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 finish line. How far did bird travel?

Answer 1

Runner is jogging at a steady 1 km/h
could you convert this into m/s ? @kate26

Answer 2

yeah but they want the answer in km?

Answer 3

We'll do that, but for finding the time in seconds. We'll need to convert speed of both bird and man into m/s
Would you do that?

Answer 4

yeah sure :) hold on

Answer 5

0.277778 m/s and 0.833333 m/s

Answer 6

OK, Now I'll explain you the scenario.

Answer 7

Runner is steadily jogging towards the finish line, which is 0.88km
At this moment the bird starts flying from the runner's position to the finish line.
It'll take 0.88/3 hours to reach the finish line.
let it be on the finish line, runner would have covered a distance of 0.88/3 * 1 km

do you get this?

Answer 8

yeah i do

Answer 9

Now the bird will return towards the runner. Let it takes time t
The runner will run for a distance 1*t for during this
now we know that
\[0.88/3+1*t+3*t=0.88\]
do you get my point and cold you find t from this?

Answer 10

umm i think so. let me try it out