Two trains

The train runs at speed v1 = 72 km/h. The passenger, sitting in the train, observed that a train long l = 75m in 3 s passed on the other track in the opposite direction. Calculate the speed of this train.

Correct result:

v₂ =  18 km/h

Solution:

$$\begin{gathered} v_1=72\text{ km/h}\to \text{ m/s}=72\mathrm{/}3.6\text{ m/s}=20\text{ m/s } \\ l=75\text{ m } \\ t=3\text{ s } \\ t={\displaystyle \frac{l}{v_1+v_2}} \\ {v}_1\cdot t+v_2\cdot t=l \\ {v}_{22}={\displaystyle \frac{l-v_1\cdot t}{t}}={\displaystyle \frac{75-20\cdot 3}{3}}=5\text{ m/s } \\ {v}_2=v_{22}\to \text{ km/h}=v_{22}\cdot 3.6\text{ km/h}=5\cdot 3.6\text{ km/h}=18\text{ km/h} \end{gathered}$$

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