A two trains problem (distance and speed)

[missrikku]

Hello, this is the problem:

Two trains, each having a speed of 30 km/hr, are headed at each other on the same straight track. A bird that can fly 60 km/hr flies off the front of one train when they are 60 km apart and heads directly back for the other train. On reaching the other train it flies directly back to the first train, and so forth. What is the total distance the bird travels?

With this information, I came up with the following:

Vbird = 60 km/hr = 16.667 m/s
Vtrain1 = 30 km/hr = Vtrain2 = 8.333 m/s
d = distance between trains when bird 1st flies off = 60km

I) I found out how long it would take for the cars to hit each other:

Vtrain1 = Vtrain2 = 8.333 m/s = 3.0 x 10^4 m / t
** 3.0 x 10^4 m came from doing d/2 or 60km/2 = 30km
t = 3600s

II) I used Vbird to find the total distance it traveled:

16.667 = total distance / 3600s
total distance = 6.0 x 10^4 m

Giving me the ans: 6.0 x 10^4 m

Was my process for answering this problem correct?

 

[HallsofIvy]

Yes, you know the speed of the bird and you know time it was flying: the product gives the total distance flown.

Of course you could try to do it the HARD way: calculate each leg back and forth and do it as an infinite series!

There is an old story about a famous mathematician (VonNeumann? I've also heard it about Wiener.) that a man asked this problem of him and he thought for a few seconds and immediately gave the correct answer. The man chuckled and said "A lot of people try to do that by summing the infinite series." VonNeumann looked puzzled and said "But I did sum an infinite series!"

(You are now to roll on the floor laughing!)

 

[M98Ranger]

Yes, your process for answering this problem is correct. You correctly identified the variables and used the given information to solve for the total distance the bird traveled. Your calculation for the time it takes for the trains to hit each other is also correct. Overall, your solution is clear and accurate. Good job!