Solve Average Velocity: 2 Trains & Bird

[natezyz]

Homework Statement

Two trains, each having a speed of 34 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 51 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels before the trains collide?

Homework Equations

average speed=deltax/deltat

The Attempt at a Solution

I'm having a lot of trouble even just setting the math up for this. I have alittle picture drawn out and have everything labeled from the distance between the two trains to the bird's position, I just don't understand how to apply this to an equation much less account for the bird and train's change of position. Anyway I imagine you set it up as the point that the bird lifts off is the origin and have a variable to represent where the bird and train will meet with something like 0+x=x-51. But now looking at that it looks completely ****ed and I feel like I'm over looking some small thing that will make the lightbulb go off.

 

[Neoriginal]

Yeah I think you might be right. The half-point is 25.5km and it would take each train .75 hours (40 minutes) to collide. The bird's velocity is a given 60km/h so you would multiply 60(.75) to get 45km.

 

[kerimek]

I would approach this problem by breaking it down into smaller, more manageable parts. First, I would calculate the time it takes for the trains to collide using the formula d=rt, where d is the distance between the trains (51 km) and r is the combined speed of the two trains (68 km/h). This gives a time of approximately 0.75 hours.

Next, I would calculate the distance the bird travels in one round trip between the two trains. This would be the sum of the distance from the origin to the first train (25.5 km) and the distance from the first train to the second train (25.5 km). This gives a total distance of 51 km.

Since the bird travels this distance in 0.75 hours, its average velocity would be 51 km/0.75 h, or 68 km/h.

Finally, to find the total distance the bird travels before the trains collide, I would multiply the bird's average velocity by the time it takes for the trains to collide. This gives a total distance of approximately 51 km.