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**1. The problem statement, all variables and given/known data**

A bird, 720 km away from a train flies towards it at a speed of 120km/h. As soon as it reaches the train, it turns back towards the wall (starting position). The train travels at a speed of 15m/s towards the starting position of the bird. How much distance towards the wall will the bird cover before the train reaches it.

**3. The attempt at a solution**

15m/s= 54km/h

Thus the train takes 720/54=13.33 hours to reach the wall.

The relative velocity of the bird wrt train when travelling towards it is 54+120=174km/h

The relative velocity when travelling away from the train is 120-54=66km/h

Ratios of velocities (towards:away)=29:11

Thus the ratio of time taken in travelling towards the train to away from the train =11:29

Thus, the bird spent a total of [tex]\frac{29}{29+11}\times 13.33[/tex] hours travelling away from the train.

The velocity of the bird travelling away from the train is 120km/h

Thus, the distance travelled by the bird away from the train is [tex]13.33\times \frac{29}{40} \times 120=1160 km[/tex]

Which is the wrong answer. The solution is 800 km. Why?