A runner is jogging in a straight line at a steady vr= 2.2 km/hr. When the runner is L= 4 km from the ﬁnish line, a bird begins ﬂying straight from the runner to the ﬁnish line at vb= 6.6 km/hr (3 times as fast as the runner). When the bird reaches the ﬁnishline, it turns around and ﬂies directly back to the runner.

Question

A runner is jogging in a straight line at a steady vr= 2.2 km/hr. When the runner is L= 4 km from the ﬁnish line, a bird begins ﬂying straight from the runner to the ﬁnish line at vb= 6.6 km/hr (3 times as fast as the runner). When the bird reaches the ﬁnishline, it turns around and ﬂies directly back to the runner.
Q1:What cumulative distance does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a “zero” length bird), travels in a straight line, and that it can turn without loss of speed. 
Q2: 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)?I CANT UNDERSTAND please someone explain to me thank you!

Steve · Accepted Answer

part 2 of this question is easier than part 1.
For part 2, just figure how long it takes the runner to finish the race. At 2.2 km/hr, it will take 4/2.2 = 1.81 = 20/11 hours. Since the bird is flying at 6.6 km/hr for that whole time, it files 6.6 * 20/11 = 12 km

The hard part is figuring out the distance to that first encounter.
Since the bird flies 3 times as fast as the runner, when the bird gets to the finish line, the runner is only 1/3 of the way there, so the distance between the bird and the runner is 8/3 km. So, since the bird flies 3 times as fast, it will cover 3/4 of that distance, or 2 km. So its total flight is 4+2=6 km.