Two buses running towards each other on the same track are moving at a speed of 40km/hr and are separated by 80km. A bird takes it flight from the bus A and flies towards bus B at a constant speed of 100km/hr. Once it reaches bus Y, it turns and starts flying back towards bus X. The bird keeps flying to and forth till both the buses collide. Find the distance traveled by the bird

To solve this problem, we first need to determine the time it takes for the buses to collide. We can use the formula:

time=distancerelative speedtime=relative speeddistance​

Here, the relative speed of the two buses is the sum of their speeds because they are moving towards each other.

Relative speed of the buses = $40\text{ km/hr}+40\text{ km/hr}=80\text{ km/hr}$

time=80 km80 km/hr=1 hourtime=80 km/hr80 km​=1 hour

Now, let’s find out how far the bird travels during this 1-hour period. The bird’s speed is $100\text{ km/hr}$, so it covers a distance of $100\text{ km/hr}\times 1\text{ hr}=100\text{ km}$.

However, we need to consider that the bird starts flying when the buses are 80 km apart. So, it covers $80\text{ km}$ towards the other bus before they start moving towards each other. Then, it will keep flying back and forth between the buses until they collide.

Therefore, the total distance traveled by the bird is $80\text{ km}+100\text{ km}+100\text{ km}=280\text{ km}$.