# A two trains problem (distance and speed)

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?