Calculating the length of a train

Question

In the above question, I tired to calculate the length of the train as

300/1200 + 3/1200 = 11/400 Km

But they are subtracting the above length. I'm not sure why they are doing so.

Answer 1

Relative to the man the train is traveling $27$ km/hr. In $3$ seconds it travels $27 \cdot \frac 3{3600}=\frac 9{400}$ km relative to the man.

Answer 2

For this problem, we need to recall that for relative velocities, the velocity of $A$ with respect to $B$ is given by $V_{AB}=V_{A}-V_{B}$ in this particular setting.

So, the velocity of the train with respect to the man will be $V_{TM}=V_{T}-V_{M}=30-2=27\frac{km}{h}$. From the perspective of the man, it appears that he is not moving at all while the train goes by at $27\frac{km}{h}$. It only takes three seconds for the train's caboose to pass by the man, so we need to find out how far the train traveled in three seconds from the perspective of the man, which would be the length of the train . $$27\frac{km}{h}\cdot\frac{1 h}{3600 s}\cdot3s=\frac{9}{400}km $$