Question regarding relative velocities

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Larry and Harry are driving towards each other, with Larry at 40 km/h and Harry at 30 km/h, starting 42 km apart. The relative velocity between them is 70 km/h, allowing them to meet in 0.6 hours. During this time, the pigeon flies continuously at 50 km/h, covering a total distance of 30 km before the twins meet. The solution is straightforward, as the total distance the pigeon flies can be calculated directly without needing to break down each leg of its journey. The problem confirms that the simpler method is sufficient for finding the total distance flown by the pigeon.
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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
 
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It is this simple although the other (long) way also works if you know what you're doing.
 

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