Question regarding relative velocities

[JoeWr18]

Homework Statement

Larry is driving east at 40 km/h. His twin brother Harry is driving west at 30 km/h toward Larry along the same straight road. When they are 42 km apart larry sends out a carrier pigeon, which flies at a constant speed of 50 km/h (all speeds relative to the earth) . The pidgeon flies to Harry, becomes confused and immediatley returns to Larry, becomes more confused and then flies back to Harry. This continues until the twins meet, ignoring turn around time, how far did the pigeon fly.

Homework Equations

I think its just simple gallilean addition of velocities, but there's a part of my thought process I'm doubting which I will outline below.

The Attempt at a Solution

Velocity of Larry relative to Harry= 70 km/h

Time taken for them to cover 42 Km: T= 42/70= 0.6 Hours

In this time the pigeon travels distance D= 0.6*50 = 30 km

Is it this simple or do i need to calculate the distance for each "leg" of the pigeons journey using its velocities relative to each of the drivers?

Thanks
Joe

 

[kuruman]

It is this simple although the other (long) way also works if you know what you're doing.