A runner is jogging at a steady 8.4 km/hr. When the runner is 2.6 km from the finish line, a bird begins flying from the runner to the finish line at 42 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.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 speed.

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A runner is jogging at a steady 8.4 km/hr. When the runner is 2.6 km from the finish line, a bird begins flying from the runner to the finish line at 42 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.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 speed.

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1/5Total Distance + 1/5 Remaining Distance ???
V (runner)= 8.4 km/hr Distance = 2.6 km V (bird) = 42 km/hr I know (by dividing) that it takes the bird .0619 to reach the finish line, it takes the runner .31 to get to the finish line. 2.6 - .51996= 2.08 is the distance the runner is from the finish line. So far the bird has gone 2.6 km... OBVIOUSLY... now the distance back? I cant think of it logically with the runner moving...
Hey, so imagine it a little like this. You know the time it takes for the bird to get from the runner to the finish line, that's good. Now since you know how much time that takes, you know the runner has also run that far. So what you need to find out is what point they meet at between the two of them, while they're moving towards each other. So calculate where the runner is from the finish line and put the bird at the finish line. Since you know the total distance between the two of them, it turns out that it's really not so hard. Just add their speeds together and calculate how much time it takes to travel the entire distance. That time is when they meet! To help understand why you can do this, imagine that there's a man and a bird 7 miles apart. The bird is travelling 5 mph and the man is travelling 2 mph. An hour later, how far are they? Well, the bird has gone 5 miles and the man has gone 2 miles. All that means is that the have mutually crossed 7 miles closer to each other and have met. So for this example problem, you can see how in one hour they both reach each other at the same point by combining their speeds. Make sense?

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I'm not exactly sure what you mean. The runner is moving at 8.4 km/hr. The bird 42 km/hr. They are 2.08 km away from each other. how do you set this up?
(50.4 km/hr)t=2.08km ???
Flight time of bird to finish line FL = 2.6/42 =(approx) .06hr Distance runner travels during time period = .06(8.4) = .52km Distance of runner to FL = 2.6-.52 = 2.08km Net closing speed between runner and bird = 8.4km +42 km = 50.4km Time for runner and bird to meet 2.6/50.4 = (approx) .05hr Distance covered by runner (.05)8.4 = (approx) .43 km Distance covered by bird to runner (.05)(42) = (approx) 2.1km 2.1 + 2.6 = 4.7km (its not correct) :( What am I doing wrong?
Time for runner and bird to meet 2.6/50.4 = (approx) .05hr This is wrong, instead of 2.6 you should be using 2.08 since this is how close the runner is when the bird has turned around. Your work other than that seems fine though. I got that the bird travelled 4.32 km.

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